312=(3x+x)*(x+1)

Solution for 312=(3x+x)*(x+1) equation:

312=(3x+x)(x+1)

We move all terms to the left:

312-((3x+x)(x+1))=0

We add all the numbers together, and all the variables

-((+4x)(x+1))+312=0

We multiply parentheses ..

-((+4x^2+4x))+312=0


We calculate terms in parentheses: -((+4x^2+4x)), so:

(+4x^2+4x)

We get rid of parentheses

4x^2+4x

Back to the equation:

-(4x^2+4x)


We get rid of parentheses

-4x^2-4x+312=0

a = -4; b = -4; c = +312;
Δ = b2-4ac
Δ = -42-4·(-4)·312
Δ = 5008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5008}=\sqrt{16*313}=\sqrt{16}*\sqrt{313}=4\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{313}}{2*-4}=\frac{4-4\sqrt{313}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{313}}{2*-4}=\frac{4+4\sqrt{313}}{-8}
$