(9x-7)(8x+3)=0

Solution for (9x-7)(8x+3)=0 equation:

(9x-7)(8x+3)=0

We multiply parentheses ..

(+72x^2+27x-56x-21)=0

We get rid of parentheses

72x^2+27x-56x-21=0

We add all the numbers together, and all the variables

72x^2-29x-21=0

a = 72; b = -29; c = -21;
Δ = b2-4ac
Δ = -292-4·72·(-21)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-83}{2*72}=\frac{-54}{144}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+83}{2*72}=\frac{112}{144}
=7/9
$