(8m+7)(5m+5)=90

Solution for (8m+7)(5m+5)=90 equation:

(8m+7)(5m+5)=90

We move all terms to the left:

(8m+7)(5m+5)-(90)=0

We multiply parentheses ..

(+40m^2+40m+35m+35)-90=0

We get rid of parentheses

40m^2+40m+35m+35-90=0

We add all the numbers together, and all the variables

40m^2+75m-55=0

a = 40; b = 75; c = -55;
Δ = b2-4ac
Δ = 752-4·40·(-55)
Δ = 14425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14425}=\sqrt{25*577}=\sqrt{25}*\sqrt{577}=5\sqrt{577}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-5\sqrt{577}}{2*40}=\frac{-75-5\sqrt{577}}{80}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+5\sqrt{577}}{2*40}=\frac{-75+5\sqrt{577}}{80}
$