-2a(a-6)=4(a-3)

Solution for -2a(a-6)=4(a-3) equation:

-2a(a-6)=4(a-3)

We move all terms to the left:

-2a(a-6)-(4(a-3))=0

We multiply parentheses

-2a^2+12a-(4(a-3))=0


We calculate terms in parentheses: -(4(a-3)), so:

4(a-3)

We multiply parentheses

4a-12

Back to the equation:

-(4a-12)


We get rid of parentheses

-2a^2+12a-4a+12=0

We add all the numbers together, and all the variables

-2a^2+8a+12=0

a = -2; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-2)·12
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*-2}=\frac{-8-4\sqrt{10}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*-2}=\frac{-8+4\sqrt{10}}{-4}
$