(9x-7)(2x+5)=0

Solution for (9x-7)(2x+5)=0 equation:

(9x-7)(2x+5)=0

We multiply parentheses ..

(+18x^2+45x-14x-35)=0

We get rid of parentheses

18x^2+45x-14x-35=0

We add all the numbers together, and all the variables

18x^2+31x-35=0

a = 18; b = 31; c = -35;
Δ = b2-4ac
Δ = 312-4·18·(-35)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-59}{2*18}=\frac{-90}{36}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+59}{2*18}=\frac{28}{36}
=7/9
$