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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+42x^2-30x-56x+40)=0

We get rid of parentheses

42x^2-30x-56x+40=0

We add all the numbers together, and all the variables

42x^2-86x+40=0

a = 42; b = -86; c = +40;
Δ = b2-4ac
Δ = -862-4·42·40
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-26}{2*42}=\frac{60}{84}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+26}{2*42}=\frac{112}{84}
=1+1/3
$