5x(8x+25)=90

Solution for 5x(8x+25)=90 equation:

5x(8x+25)=90

We move all terms to the left:

5x(8x+25)-(90)=0

We multiply parentheses

40x^2+125x-90=0

a = 40; b = 125; c = -90;
Δ = b2-4ac
Δ = 1252-4·40·(-90)
Δ = 30025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30025}=\sqrt{25*1201}=\sqrt{25}*\sqrt{1201}=5\sqrt{1201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-5\sqrt{1201}}{2*40}=\frac{-125-5\sqrt{1201}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+5\sqrt{1201}}{2*40}=\frac{-125+5\sqrt{1201}}{80}
$