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

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

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

We multiply parentheses ..

(+35x^2-40x+56x-64)=0

We get rid of parentheses

35x^2-40x+56x-64=0

We add all the numbers together, and all the variables

35x^2+16x-64=0

a = 35; b = 16; c = -64;
Δ = b2-4ac
Δ = 162-4·35·(-64)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-96}{2*35}=\frac{-112}{70}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+96}{2*35}=\frac{80}{70}
=1+1/7
$