180=2x(3x-5)

Solution for 180=2x(3x-5) equation:

180=2x(3x-5)

We move all terms to the left:

180-(2x(3x-5))=0


We calculate terms in parentheses: -(2x(3x-5)), so:

2x(3x-5)

We multiply parentheses

6x^2-10x

Back to the equation:

-(6x^2-10x)


We get rid of parentheses

-6x^2+10x+180=0

a = -6; b = 10; c = +180;
Δ = b2-4ac
Δ = 102-4·(-6)·180
Δ = 4420
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:

$\sqrt{\Delta}=\sqrt{4420}=\sqrt{4*1105}=\sqrt{4}*\sqrt{1105}=2\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1105}}{2*-6}=\frac{-10-2\sqrt{1105}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1105}}{2*-6}=\frac{-10+2\sqrt{1105}}{-12}
$