(8x-3)(7x+6)=0

Solution for (8x-3)(7x+6)=0 equation:

(8x-3)(7x+6)=0

We multiply parentheses ..

(+56x^2+48x-21x-18)=0

We get rid of parentheses

56x^2+48x-21x-18=0

We add all the numbers together, and all the variables

56x^2+27x-18=0

a = 56; b = 27; c = -18;
Δ = b2-4ac
Δ = 272-4·56·(-18)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-69}{2*56}=\frac{-96}{112}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+69}{2*56}=\frac{42}{112}
=3/8
$