((x+5)*(x))/2=75

Solution for ((x+5)*(x))/2=75 equation:

((x+5)(x))/2=75

We move all terms to the left:

((x+5)(x))/2-(75)=0

We multiply all the terms by the denominator


((x+5)x)-75*2=0


We calculate terms in parentheses: +((x+5)x), so:

(x+5)x

We multiply parentheses

x^2+5x

Back to the equation:

+(x^2+5x)


We add all the numbers together, and all the variables

(x^2+5x)-150=0

We get rid of parentheses

x^2+5x-150=0

a = 1; b = 5; c = -150;
Δ = b2-4ac
Δ = 52-4·1·(-150)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*1}=\frac{20}{2}
=10
$