(2x+7)*(3x-2)=0

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

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

We multiply parentheses ..

(+6x^2-4x+21x-14)=0

We get rid of parentheses

6x^2-4x+21x-14=0

We add all the numbers together, and all the variables

6x^2+17x-14=0

a = 6; b = 17; c = -14;
Δ = b2-4ac
Δ = 172-4·6·(-14)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*6}=\frac{8}{12}
=2/3
$