(7y+8)(8y+7)=90

Solution for (7y+8)(8y+7)=90 equation:

(7y+8)(8y+7)=90

We move all terms to the left:

(7y+8)(8y+7)-(90)=0

We multiply parentheses ..

(+56y^2+49y+64y+56)-90=0

We get rid of parentheses

56y^2+49y+64y+56-90=0

We add all the numbers together, and all the variables

56y^2+113y-34=0

a = 56; b = 113; c = -34;
Δ = b2-4ac
Δ = 1132-4·56·(-34)
Δ = 20385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20385}=\sqrt{9*2265}=\sqrt{9}*\sqrt{2265}=3\sqrt{2265}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-3\sqrt{2265}}{2*56}=\frac{-113-3\sqrt{2265}}{112}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+3\sqrt{2265}}{2*56}=\frac{-113+3\sqrt{2265}}{112}
$