(((8+x)x)/2)-600=0

Solution for (((8+x)x)/2)-600=0 equation:

(((8+x)x)/2)-600=0

We add all the numbers together, and all the variables

(((x+8)x)/2)-600=0

We multiply all the terms by the denominator


(((x+8)x)-600*2)=0


We calculate terms in parentheses: +(((x+8)x)-600*2), so:

((x+8)x)-600*2

We add all the numbers together, and all the variables

((x+8)x)-1200


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

(x+8)x

We multiply parentheses

x^2+8x

Back to the equation:

+(x^2+8x)


We get rid of parentheses

x^2+8x-1200

Back to the equation:

+(x^2+8x-1200)


We get rid of parentheses

x^2+8x-1200=0

a = 1; b = 8; c = -1200;
Δ = b2-4ac
Δ = 82-4·1·(-1200)
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{19}}{2*1}=\frac{-8-16\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{19}}{2*1}=\frac{-8+16\sqrt{19}}{2}
$