x(x+8)/2=45

Solution for x(x+8)/2=45 equation:

x(x+8)/2=45

We move all terms to the left:

x(x+8)/2-(45)=0

We multiply all the terms by the denominator


x(x+8)-45*2=0

We add all the numbers together, and all the variables

x(x+8)-90=0

We multiply parentheses

x^2+8x-90=0

a = 1; b = 8; c = -90;
Δ = b2-4ac
Δ = 82-4·1·(-90)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{106}}{2*1}=\frac{-8-2\sqrt{106}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{106}}{2*1}=\frac{-8+2\sqrt{106}}{2}
$