100=2x(x-3)

Solution for 100=2x(x-3) equation:

100=2x(x-3)

We move all terms to the left:

100-(2x(x-3))=0


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

2x(x-3)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

-2x^2+6x+100=0

a = -2; b = 6; c = +100;
Δ = b2-4ac
Δ = 62-4·(-2)·100
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{209}}{2*-2}=\frac{-6-2\sqrt{209}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{209}}{2*-2}=\frac{-6+2\sqrt{209}}{-4}
$