360=x(x-3)+(x+8)+(x-3)

Solution for 360=x(x-3)+(x+8)+(x-3) equation:

360=x(x-3)+(x+8)+(x-3)

We move all terms to the left:

360-(x(x-3)+(x+8)+(x-3))=0


We calculate terms in parentheses: -(x(x-3)+(x+8)+(x-3)), so:

x(x-3)+(x+8)+(x-3)

We multiply parentheses

x^2-3x+(x+8)+(x-3)

We get rid of parentheses

x^2-3x+x+x+8-3

We add all the numbers together, and all the variables

x^2-1x+5

Back to the equation:

-(x^2-1x+5)


We get rid of parentheses

-x^2+1x-5+360=0

We add all the numbers together, and all the variables

-1x^2+x+355=0

a = -1; b = 1; c = +355;
Δ = b2-4ac
Δ = 12-4·(-1)·355
Δ = 1421
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:

$\sqrt{\Delta}=\sqrt{1421}=\sqrt{49*29}=\sqrt{49}*\sqrt{29}=7\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{29}}{2*-1}=\frac{-1-7\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{29}}{2*-1}=\frac{-1+7\sqrt{29}}{-2}
$