x^2-32x+240=84

Solution for x^2-32x+240=84 equation:

x^2-32x+240=84

We move all terms to the left:

x^2-32x+240-(84)=0

We add all the numbers together, and all the variables

x^2-32x+156=0

a = 1; b = -32; c = +156;
Δ = b2-4ac
Δ = -322-4·1·156
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20}{2*1}=\frac{52}{2}
=26
$