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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-6x^2+12x+15x-30)=0

We get rid of parentheses

-6x^2+12x+15x-30=0

We add all the numbers together, and all the variables

-6x^2+27x-30=0

a = -6; b = 27; c = -30;
Δ = b2-4ac
Δ = 272-4·(-6)·(-30)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3}{2*-6}=\frac{-24}{-12}
=+2
$