6^2=(x)(x+x-3)

Solution for 6^2=(x)(x+x-3) equation:

6^2=(x)(x+x-3)

We move all terms to the left:

6^2-((x)(x+x-3))=0

We add all the numbers together, and all the variables

-(x(2x-3))+6^2=0

We add all the numbers together, and all the variables

-(x(2x-3))+36=0


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

x(2x-3)

We multiply parentheses

2x^2-3x

Back to the equation:

-(2x^2-3x)


We get rid of parentheses

-2x^2+3x+36=0

a = -2; b = 3; c = +36;
Δ = b2-4ac
Δ = 32-4·(-2)·36
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*-2}=\frac{-3-3\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*-2}=\frac{-3+3\sqrt{33}}{-4}
$