(6x+5)(2x-3)=0

Solution for (6x+5)(2x-3)=0 equation:

(6x+5)(2x-3)=0

We multiply parentheses ..

(+12x^2-18x+10x-15)=0

We get rid of parentheses

12x^2-18x+10x-15=0

We add all the numbers together, and all the variables

12x^2-8x-15=0

a = 12; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·12·(-15)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*12}=\frac{-20}{24}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*12}=\frac{36}{24}
=1+1/2
$