(9x-8)(2x-7)=0

Solution for (9x-8)(2x-7)=0 equation:

(9x-8)(2x-7)=0

We multiply parentheses ..

(+18x^2-63x-16x+56)=0

We get rid of parentheses

18x^2-63x-16x+56=0

We add all the numbers together, and all the variables

18x^2-79x+56=0

a = 18; b = -79; c = +56;
Δ = b2-4ac
Δ = -792-4·18·56
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-47}{2*18}=\frac{32}{36}
=8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+47}{2*18}=\frac{126}{36}
=3+1/2
$