(2x-7)(3x-1)=7

Solution for (2x-7)(3x-1)=7 equation:

(2x-7)(3x-1)=7

We move all terms to the left:

(2x-7)(3x-1)-(7)=0

We multiply parentheses ..

(+6x^2-2x-21x+7)-7=0

We get rid of parentheses

6x^2-2x-21x+7-7=0

We add all the numbers together, and all the variables

6x^2-23x=0

a = 6; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·6·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*6}=\frac{46}{12}
=3+5/6
$