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

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

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

We multiply parentheses ..

(-2x^2-14x+3x+21)=0

We get rid of parentheses

-2x^2-14x+3x+21=0

We add all the numbers together, and all the variables

-2x^2-11x+21=0

a = -2; b = -11; c = +21;
Δ = b2-4ac
Δ = -112-4·(-2)·21
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-2}=\frac{28}{-4}
=-7
$