(8x-2)(10x+15)=10

Solution for (8x-2)(10x+15)=10 equation:

(8x-2)(10x+15)=10

We move all terms to the left:

(8x-2)(10x+15)-(10)=0

We multiply parentheses ..

(+80x^2+120x-20x-30)-10=0

We get rid of parentheses

80x^2+120x-20x-30-10=0

We add all the numbers together, and all the variables

80x^2+100x-40=0

a = 80; b = 100; c = -40;
Δ = b2-4ac
Δ = 1002-4·80·(-40)
Δ = 22800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{22800}=\sqrt{400*57}=\sqrt{400}*\sqrt{57}=20\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{57}}{2*80}=\frac{-100-20\sqrt{57}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{57}}{2*80}=\frac{-100+20\sqrt{57}}{160}
$