(x*(x+8))/2=212.5

Solution for (x*(x+8))/2=212.5 equation:

(x(x+8))/2=212.5

We move all terms to the left:

(x(x+8))/2-(212.5)=0

We add all the numbers together, and all the variables

(x(x+8))/2-212.5=0

We multiply all the terms by the denominator


(x(x+8))-(212.5)*2=0


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

x(x+8)

We multiply parentheses

x^2+8x

Back to the equation:

+(x^2+8x)


We add all the numbers together, and all the variables

(x^2+8x)-425=0

We get rid of parentheses

x^2+8x-425=0

a = 1; b = 8; c = -425;
Δ = b2-4ac
Δ = 82-4·1·(-425)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-42}{2*1}=\frac{-50}{2}
=-25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+42}{2*1}=\frac{34}{2}
=17
$