X^2+(3-2a)X-6a=0

Solution for X^2+(3-2a)X-6a=0 equation:

X^2+(3-2X)X-6X=0

We add all the numbers together, and all the variables

X^2+(-2X+3)X-6X=0

We add all the numbers together, and all the variables

X^2-6X+(-2X+3)X=0

We multiply parentheses

X^2-2X^2-6X+3X=0

We add all the numbers together, and all the variables

-1X^2-3X=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
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{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$