6(6+12)=x(x+14)

Solution for 6(6+12)=x(x+14) equation:

6(6+12)=x(x+14)

We move all terms to the left:

6(6+12)-(x(x+14))=0

We add all the numbers together, and all the variables

-(x(x+14))+618=0


We calculate terms in parentheses: -(x(x+14)), so:

x(x+14)

We multiply parentheses

x^2+14x

Back to the equation:

-(x^2+14x)


We get rid of parentheses

-x^2-14x+618=0

We add all the numbers together, and all the variables

-1x^2-14x+618=0

a = -1; b = -14; c = +618;
Δ = b2-4ac
Δ = -142-4·(-1)·618
Δ = 2668
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:

$\sqrt{\Delta}=\sqrt{2668}=\sqrt{4*667}=\sqrt{4}*\sqrt{667}=2\sqrt{667}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{667}}{2*-1}=\frac{14-2\sqrt{667}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{667}}{2*-1}=\frac{14+2\sqrt{667}}{-2}
$