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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+8x-12=0

a = 15; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·15·(-12)
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*15}=\frac{-36}{30}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*15}=\frac{20}{30}
=2/3
$