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

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

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

We multiply parentheses ..

(+42x^2-35x+48x-40)=0

We get rid of parentheses

42x^2-35x+48x-40=0

We add all the numbers together, and all the variables

42x^2+13x-40=0

a = 42; b = 13; c = -40;
Δ = b2-4ac
Δ = 132-4·42·(-40)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-83}{2*42}=\frac{-96}{84}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+83}{2*42}=\frac{70}{84}
=5/6
$