(8x-5)(10x-17)=0

Solution for (8x-5)(10x-17)=0 equation:

(8x-5)(10x-17)=0

We multiply parentheses ..

(+80x^2-136x-50x+85)=0

We get rid of parentheses

80x^2-136x-50x+85=0

We add all the numbers together, and all the variables

80x^2-186x+85=0

a = 80; b = -186; c = +85;
Δ = b2-4ac
Δ = -1862-4·80·85
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-86}{2*80}=\frac{100}{160}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+86}{2*80}=\frac{272}{160}
=1+7/10
$