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

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

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

We multiply parentheses ..

(+48x^2-30x+56x-35)=0

We get rid of parentheses

48x^2-30x+56x-35=0

We add all the numbers together, and all the variables

48x^2+26x-35=0

a = 48; b = 26; c = -35;
Δ = b2-4ac
Δ = 262-4·48·(-35)
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-86}{2*48}=\frac{-112}{96}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+86}{2*48}=\frac{60}{96}
=5/8
$