X^2-14x=2x-32

Solution for X^2-14x=2x-32 equation:

X^2-14X=2X-32

We move all terms to the left:

X^2-14X-(2X-32)=0

We get rid of parentheses

X^2-14X-2X+32=0

We add all the numbers together, and all the variables

X^2-16X+32=0

a = 1; b = -16; c = +32;
Δ = b2-4ac
Δ = -162-4·1·32
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{2}}{2*1}=\frac{16-8\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{2}}{2*1}=\frac{16+8\sqrt{2}}{2}
$