(8x-6)(2x-7)=0

Solution for (8x-6)(2x-7)=0 equation:

(8x-6)(2x-7)=0

We multiply parentheses ..

(+16x^2-56x-12x+42)=0

We get rid of parentheses

16x^2-56x-12x+42=0

We add all the numbers together, and all the variables

16x^2-68x+42=0

a = 16; b = -68; c = +42;
Δ = b2-4ac
Δ = -682-4·16·42
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-44}{2*16}=\frac{24}{32}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+44}{2*16}=\frac{112}{32}
=3+1/2
$