90=5x(x+54)

Solution for 90=5x(x+54) equation:

90=5x(x+54)

We move all terms to the left:

90-(5x(x+54))=0


We calculate terms in parentheses: -(5x(x+54)), so:

5x(x+54)

We multiply parentheses

5x^2+270x

Back to the equation:

-(5x^2+270x)


We get rid of parentheses

-5x^2-270x+90=0

a = -5; b = -270; c = +90;
Δ = b2-4ac
Δ = -2702-4·(-5)·90
Δ = 74700
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:

$\sqrt{\Delta}=\sqrt{74700}=\sqrt{900*83}=\sqrt{900}*\sqrt{83}=30\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-30\sqrt{83}}{2*-5}=\frac{270-30\sqrt{83}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+30\sqrt{83}}{2*-5}=\frac{270+30\sqrt{83}}{-10}
$