(7r+6)(8r+8)=90

Solution for (7r+6)(8r+8)=90 equation:

(7r+6)(8r+8)=90

We move all terms to the left:

(7r+6)(8r+8)-(90)=0

We multiply parentheses ..

(+56r^2+56r+48r+48)-90=0

We get rid of parentheses

56r^2+56r+48r+48-90=0

We add all the numbers together, and all the variables

56r^2+104r-42=0

a = 56; b = 104; c = -42;
Δ = b2-4ac
Δ = 1042-4·56·(-42)
Δ = 20224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20224}=\sqrt{256*79}=\sqrt{256}*\sqrt{79}=16\sqrt{79}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-16\sqrt{79}}{2*56}=\frac{-104-16\sqrt{79}}{112}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+16\sqrt{79}}{2*56}=\frac{-104+16\sqrt{79}}{112}
$