4x(x+45)=90

Solution for 4x(x+45)=90 equation:

4x(x+45)=90

We move all terms to the left:

4x(x+45)-(90)=0

We multiply parentheses

4x^2+180x-90=0

a = 4; b = 180; c = -90;
Δ = b2-4ac
Δ = 1802-4·4·(-90)
Δ = 33840
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:

$\sqrt{\Delta}=\sqrt{33840}=\sqrt{144*235}=\sqrt{144}*\sqrt{235}=12\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{235}}{2*4}=\frac{-180-12\sqrt{235}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{235}}{2*4}=\frac{-180+12\sqrt{235}}{8}
$