7y^2+13y=(8y)^2

Solution for 7y^2+13y=(8y)^2 equation:

7y^2+13y=(8y)^2

We move all terms to the left:

7y^2+13y-((8y)^2)=0

determiningTheFunctionDomain
7y^2+13y-8y^2=0

We add all the numbers together, and all the variables

7y^2-8y^2+13y=0

We add all the numbers together, and all the variables

-1y^2+13y=0

a = -1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1}=\frac{-26}{-2}
=+13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1}=\frac{0}{-2}
=0
$