(3x-7)(x-6)=4

Solution for (3x-7)(x-6)=4 equation:

(3x-7)(x-6)=4

We move all terms to the left:

(3x-7)(x-6)-(4)=0

We multiply parentheses ..

(+3x^2-18x-7x+42)-4=0

We get rid of parentheses

3x^2-18x-7x+42-4=0

We add all the numbers together, and all the variables

3x^2-25x+38=0

a = 3; b = -25; c = +38;
Δ = b2-4ac
Δ = -252-4·3·38
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-13}{2*3}=\frac{12}{6}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+13}{2*3}=\frac{38}{6}
=6+1/3
$