(5x-8)(7x+6)=0

Solution for (5x-8)(7x+6)=0 equation:

(5x-8)(7x+6)=0

We multiply parentheses ..

(+35x^2+30x-56x-48)=0

We get rid of parentheses

35x^2+30x-56x-48=0

We add all the numbers together, and all the variables

35x^2-26x-48=0

a = 35; b = -26; c = -48;
Δ = b2-4ac
Δ = -262-4·35·(-48)
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{-(-26)-86}{2*35}=\frac{-60}{70}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+86}{2*35}=\frac{112}{70}
=1+3/5
$