-2(u+6)6u=4(u-3)

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

-2(u+6)6u=4(u-3)

We move all terms to the left:

-2(u+6)6u-(4(u-3))=0

We multiply parentheses

-12u^2-72u-(4(u-3))=0


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

4(u-3)

We multiply parentheses

4u-12

Back to the equation:

-(4u-12)


We get rid of parentheses

-12u^2-72u-4u+12=0

We add all the numbers together, and all the variables

-12u^2-76u+12=0

a = -12; b = -76; c = +12;
Δ = b2-4ac
Δ = -762-4·(-12)·12
Δ = 6352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6352}=\sqrt{16*397}=\sqrt{16}*\sqrt{397}=4\sqrt{397}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{397}}{2*-12}=\frac{76-4\sqrt{397}}{-24}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{397}}{2*-12}=\frac{76+4\sqrt{397}}{-24}
$