(9x+10)(8x-3)=0

Solution for (9x+10)(8x-3)=0 equation:

(9x+10)(8x-3)=0

We multiply parentheses ..

(+72x^2-27x+80x-30)=0

We get rid of parentheses

72x^2-27x+80x-30=0

We add all the numbers together, and all the variables

72x^2+53x-30=0

a = 72; b = 53; c = -30;
Δ = b2-4ac
Δ = 532-4·72·(-30)
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-107}{2*72}=\frac{-160}{144}
=-1+1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+107}{2*72}=\frac{54}{144}
=3/8
$