1086=6x(x+17)

Solution for 1086=6x(x+17) equation:

1086=6x(x+17)

We move all terms to the left:

1086-(6x(x+17))=0


We calculate terms in parentheses: -(6x(x+17)), so:

6x(x+17)

We multiply parentheses

6x^2+102x

Back to the equation:

-(6x^2+102x)


We get rid of parentheses

-6x^2-102x+1086=0

a = -6; b = -102; c = +1086;
Δ = b2-4ac
Δ = -1022-4·(-6)·1086
Δ = 36468
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:

$\sqrt{\Delta}=\sqrt{36468}=\sqrt{36*1013}=\sqrt{36}*\sqrt{1013}=6\sqrt{1013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{1013}}{2*-6}=\frac{102-6\sqrt{1013}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{1013}}{2*-6}=\frac{102+6\sqrt{1013}}{-12}
$