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

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

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

We add all the numbers together, and all the variables

(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+28x-12=0

a = -15; b = 28; c = -12;
Δ = b2-4ac
Δ = 282-4·(-15)·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8}{2*-15}=\frac{-36}{-30}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8}{2*-15}=\frac{-20}{-30}
=2/3
$