x(x+8)/2=90

Solution for x(x+8)/2=90 equation:

x(x+8)/2=90

We move all terms to the left:

x(x+8)/2-(90)=0

We multiply all the terms by the denominator


x(x+8)-90*2=0

We add all the numbers together, and all the variables

x(x+8)-180=0

We multiply parentheses

x^2+8x-180=0

a = 1; b = 8; c = -180;
Δ = b2-4ac
Δ = 82-4·1·(-180)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*1}=\frac{20}{2}
=10
$