(X-3)(8x+5)=0

Solution for (X-3)(8x+5)=0 equation:

(X-3)(8X+5)=0

We multiply parentheses ..

(+8X^2+5X-24X-15)=0

We get rid of parentheses

8X^2+5X-24X-15=0

We add all the numbers together, and all the variables

8X^2-19X-15=0

a = 8; b = -19; c = -15;
Δ = b2-4ac
Δ = -192-4·8·(-15)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-29}{2*8}=\frac{-10}{16}
=-5/8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+29}{2*8}=\frac{48}{16}
=3
$