(3x-5)(6x+8)=0

Solution for (3x-5)(6x+8)=0 equation:

(3x-5)(6x+8)=0

We multiply parentheses ..

(+18x^2+24x-30x-40)=0

We get rid of parentheses

18x^2+24x-30x-40=0

We add all the numbers together, and all the variables

18x^2-6x-40=0

a = 18; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·18·(-40)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-54}{2*18}=\frac{-48}{36}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+54}{2*18}=\frac{60}{36}
=1+2/3
$