90=5x(x-6)

Solution for 90=5x(x-6) equation:

90=5x(x-6)

We move all terms to the left:

90-(5x(x-6))=0


We calculate terms in parentheses: -(5x(x-6)), so:

5x(x-6)

We multiply parentheses

5x^2-30x

Back to the equation:

-(5x^2-30x)


We get rid of parentheses

-5x^2+30x+90=0

a = -5; b = 30; c = +90;
Δ = b2-4ac
Δ = 302-4·(-5)·90
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{3}}{2*-5}=\frac{-30-30\sqrt{3}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{3}}{2*-5}=\frac{-30+30\sqrt{3}}{-10}
$