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

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

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

We multiply parentheses ..

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

We get rid of parentheses

-12x^2-10x+18x+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{-36}{-24}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*-12}=\frac{20}{-24}
=-5/6
$