(4x-3)(5x+7)=0

Solution for (4x-3)(5x+7)=0 equation:

(4x-3)(5x+7)=0

We multiply parentheses ..

(+20x^2+28x-15x-21)=0

We get rid of parentheses

20x^2+28x-15x-21=0

We add all the numbers together, and all the variables

20x^2+13x-21=0

a = 20; b = 13; c = -21;
Δ = b2-4ac
Δ = 132-4·20·(-21)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-43}{2*20}=\frac{-56}{40}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+43}{2*20}=\frac{30}{40}
=3/4
$