(7x-8)(5x+9)=0

Solution for (7x-8)(5x+9)=0 equation:

(7x-8)(5x+9)=0

We multiply parentheses ..

(+35x^2+63x-40x-72)=0

We get rid of parentheses

35x^2+63x-40x-72=0

We add all the numbers together, and all the variables

35x^2+23x-72=0

a = 35; b = 23; c = -72;
Δ = b2-4ac
Δ = 232-4·35·(-72)
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-103}{2*35}=\frac{-126}{70}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+103}{2*35}=\frac{80}{70}
=1+1/7
$