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

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

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

We move all terms to the left:

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

We multiply parentheses

-12u^2-48u-(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^2-48u-4u+12=0

We add all the numbers together, and all the variables

-12u^2-52u+12=0

a = -12; b = -52; c = +12;
Δ = b2-4ac
Δ = -522-4·(-12)·12
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{205}}{2*-12}=\frac{52-4\sqrt{205}}{-24}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{205}}{2*-12}=\frac{52+4\sqrt{205}}{-24}
$