2^{7}times sqrtfrac{1}{4}

Help with solution to 2 variable quadratic equation.
Could someone help with an explanation on how to treat the equation below, please? A solution I have read uses the discriminant to find the range i.e.
${\displaystyle 9-20y^2-16y>\text{or}=0}$. To me this means treating the variable Y as a constant , is that "acceptable" ? does anyone have a reference for these equations ?
${\displaystyle y{x}^2+5y-3x+4=0}$
rewrite as ${\displaystyle y{x}^2-3x+(5y+4)=0}$

How can I prove that if ${\displaystyle x^2+bx+c}$ is factorable, then ${\displaystyle x^2-bx+c}$ is also factorable?

To express: The given signed numbers as absolute values.
Difference of the smaller and the larger absolute value.
Given:
[-6, +6] is given as a pair of signed numbers.

Prove or disprove that the system of inequalities
$a,b,d,e,f,g,h,i>0$
$a+e-i>0$
$ae-ai-bd-ei-fh>0$
$-aei-hfa+bdi-gbf>0$
is inconsistent.

Find an equation in slope-intercept form of the line passing through $(3,-4)$ with x-intercer equal to 7

A high school quadratic problem
"If ${\displaystyle a_1,a_2,a_3,\dots }$, an are distinct non-zero numbers such that
${\displaystyle \left(\sum _{k=1}^{n-1}\left\{{\left\{a_k\right\}}^2\right\}\right)x^2+2\left(\sum _{k=1}^{n-1}{a}_k{a}_{k+1}\right)x+\left(\sum _{k=2}^n\left\{{\left\{a_k\right\}}^2\right\}\right)\le 0}$

Boy is choosing between two exercise routines:
In Routine 1, he burns 30 calories walking. He then runs at a rate that burns 11.75 calories per minute.
In Routine 2, he does only running, burning 15.5 calories per minute.
For what amounts of time spent running will Routine 1 burn more calories than Routine 2? Use t for the number of minutes spent running, and solve for t.