(3x-8)(x-4)=7

Solution for (3x-8)(x-4)=7 equation:

(3x-8)(x-4)=7

We move all terms to the left:

(3x-8)(x-4)-(7)=0

We multiply parentheses ..

(+3x^2-12x-8x+32)-7=0

We get rid of parentheses

3x^2-12x-8x+32-7=0

We add all the numbers together, and all the variables

3x^2-20x+25=0

a = 3; b = -20; c = +25;
Δ = b2-4ac
Δ = -202-4·3·25
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*3}=\frac{10}{6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*3}=\frac{30}{6}
=5
$