(6x-20)*(7x-8)=0

Solution for (6x-20)*(7x-8)=0 equation:

(6x-20)(7x-8)=0

We multiply parentheses ..

(+42x^2-48x-140x+160)=0

We get rid of parentheses

42x^2-48x-140x+160=0

We add all the numbers together, and all the variables

42x^2-188x+160=0

a = 42; b = -188; c = +160;
Δ = b2-4ac
Δ = -1882-4·42·160
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-188)-92}{2*42}=\frac{96}{84}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-188)+92}{2*42}=\frac{280}{84}
=3+1/3
$