125=(3x-8)(x-6)

Solution for 125=(3x-8)(x-6) equation:

125=(3x-8)(x-6)

We move all terms to the left:

125-((3x-8)(x-6))=0

We multiply parentheses ..

-((+3x^2-18x-8x+48))+125=0


We calculate terms in parentheses: -((+3x^2-18x-8x+48)), so:

(+3x^2-18x-8x+48)

We get rid of parentheses

3x^2-18x-8x+48

We add all the numbers together, and all the variables

3x^2-26x+48

Back to the equation:

-(3x^2-26x+48)


We get rid of parentheses

-3x^2+26x-48+125=0

We add all the numbers together, and all the variables

-3x^2+26x+77=0

a = -3; b = 26; c = +77;
Δ = b2-4ac
Δ = 262-4·(-3)·77
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-40}{2*-3}=\frac{-66}{-6}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+40}{2*-3}=\frac{14}{-6}
=-2+1/3
$