(3x-7)(2x+1)-23=0

Solution for (3x-7)(2x+1)-23=0 equation:

(3x-7)(2x+1)-23=0

We multiply parentheses ..

(+6x^2+3x-14x-7)-23=0

We get rid of parentheses

6x^2+3x-14x-7-23=0

We add all the numbers together, and all the variables

6x^2-11x-30=0

a = 6; b = -11; c = -30;
Δ = b2-4ac
Δ = -112-4·6·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*6}=\frac{40}{12}
=3+1/3
$