(8x+3)(x-2)=0

Solution for (8x+3)(x-2)=0 equation:

(8x+3)(x-2)=0

We multiply parentheses ..

(+8x^2-16x+3x-6)=0

We get rid of parentheses

8x^2-16x+3x-6=0

We add all the numbers together, and all the variables

8x^2-13x-6=0

a = 8; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·8·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*8}=\frac{-6}{16}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*8}=\frac{32}{16}
=2
$