4x(9x+25)=90

Solution for 4x(9x+25)=90 equation:

4x(9x+25)=90

We move all terms to the left:

4x(9x+25)-(90)=0

We multiply parentheses

36x^2+100x-90=0

a = 36; b = 100; c = -90;
Δ = b2-4ac
Δ = 1002-4·36·(-90)
Δ = 22960
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:

$\sqrt{\Delta}=\sqrt{22960}=\sqrt{16*1435}=\sqrt{16}*\sqrt{1435}=4\sqrt{1435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{1435}}{2*36}=\frac{-100-4\sqrt{1435}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{1435}}{2*36}=\frac{-100+4\sqrt{1435}}{72}
$