20^2=x(x+x-6)

Solution for 20^2=x(x+x-6) equation:

20^2=x(x+x-6)

We move all terms to the left:

20^2-(x(x+x-6))=0

We add all the numbers together, and all the variables

-(x(2x-6))+20^2=0

We add all the numbers together, and all the variables

-(x(2x-6))+400=0


We calculate terms in parentheses: -(x(2x-6)), so:

x(2x-6)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

-2x^2+6x+400=0

a = -2; b = 6; c = +400;
Δ = b2-4ac
Δ = 62-4·(-2)·400
Δ = 3236
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:

$\sqrt{\Delta}=\sqrt{3236}=\sqrt{4*809}=\sqrt{4}*\sqrt{809}=2\sqrt{809}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{809}}{2*-2}=\frac{-6-2\sqrt{809}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{809}}{2*-2}=\frac{-6+2\sqrt{809}}{-4}
$