(2x-7)(-3x+12)=0

Solution for (2x-7)(-3x+12)=0 equation:

(2x-7)(-3x+12)=0

We multiply parentheses ..

(-6x^2+24x+21x-84)=0

We get rid of parentheses

-6x^2+24x+21x-84=0

We add all the numbers together, and all the variables

-6x^2+45x-84=0

a = -6; b = 45; c = -84;
Δ = b2-4ac
Δ = 452-4·(-6)·(-84)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3}{2*-6}=\frac{-42}{-12}
=3+1/2
$