(2x-7)(3x+8)=0

Solution for (2x-7)(3x+8)=0 equation:

(2x-7)(3x+8)=0

We multiply parentheses ..

(+6x^2+16x-21x-56)=0

We get rid of parentheses

6x^2+16x-21x-56=0

We add all the numbers together, and all the variables

6x^2-5x-56=0

a = 6; b = -5; c = -56;
Δ = b2-4ac
Δ = -52-4·6·(-56)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-37}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+37}{2*6}=\frac{42}{12}
=3+1/2
$