(X-14)(X-8)=12x

Solution for (X-14)(X-8)=12x equation:

(X-14)(X-8)=12X

We move all terms to the left:

(X-14)(X-8)-(12X)=0

We add all the numbers together, and all the variables

-12X+(X-14)(X-8)=0

We multiply parentheses ..

(+X^2-8X-14X+112)-12X=0

We get rid of parentheses

X^2-8X-14X-12X+112=0

We add all the numbers together, and all the variables

X^2-34X+112=0

a = 1; b = -34; c = +112;
Δ = b2-4ac
Δ = -342-4·1·112
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{177}}{2*1}=\frac{34-2\sqrt{177}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{177}}{2*1}=\frac{34+2\sqrt{177}}{2}
$