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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

42x^2-44x-16=0

a = 42; b = -44; c = -16;
Δ = b2-4ac
Δ = -442-4·42·(-16)
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-68}{2*42}=\frac{-24}{84}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+68}{2*42}=\frac{112}{84}
=1+1/3
$