(8+x)x/2=40

Solution for (8+x)x/2=40 equation:

(8+x)x/2=40

We move all terms to the left:

(8+x)x/2-(40)=0

We add all the numbers together, and all the variables

(x+8)x/2-40=0

We multiply all the terms by the denominator


(x+8)x-40*2=0

We add all the numbers together, and all the variables

(x+8)x-80=0

We multiply parentheses

x^2+8x-80=0

a = 1; b = 8; c = -80;
Δ = b2-4ac
Δ = 82-4·1·(-80)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*1}=\frac{-8-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*1}=\frac{-8+8\sqrt{6}}{2}
$