3u^2+7u-6=7(6+u)

Solution for 3u^2+7u-6=7(6+u) equation:

3u^2+7u-6=7(6+u)

We move all terms to the left:

3u^2+7u-6-(7(6+u))=0

We add all the numbers together, and all the variables

3u^2+7u-(7(u+6))-6=0


We calculate terms in parentheses: -(7(u+6)), so:

7(u+6)

We multiply parentheses

7u+42

Back to the equation:

-(7u+42)


We get rid of parentheses

3u^2+7u-7u-42-6=0

We add all the numbers together, and all the variables

3u^2-48=0

a = 3; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·3·(-48)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*3}=\frac{-24}{6}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*3}=\frac{24}{6}
=4
$