90=5x(2x-30)

Solution for 90=5x(2x-30) equation:

90=5x(2x-30)

We move all terms to the left:

90-(5x(2x-30))=0


We calculate terms in parentheses: -(5x(2x-30)), so:

5x(2x-30)

We multiply parentheses

10x^2-150x

Back to the equation:

-(10x^2-150x)


We get rid of parentheses

-10x^2+150x+90=0

a = -10; b = 150; c = +90;
Δ = b2-4ac
Δ = 1502-4·(-10)·90
Δ = 26100
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:

$\sqrt{\Delta}=\sqrt{26100}=\sqrt{900*29}=\sqrt{900}*\sqrt{29}=30\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-30\sqrt{29}}{2*-10}=\frac{-150-30\sqrt{29}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+30\sqrt{29}}{2*-10}=\frac{-150+30\sqrt{29}}{-20}
$