X^2+6x=-11/6

Solution for X^2+6x=-11/6 equation:

X^2+6X=-11/6

We move all terms to the left:

X^2+6X-(-11/6)=0

We get rid of parentheses

X^2+6X+11/6=0

We multiply all the terms by the denominator


X^2*6+6X*6+11=0

Wy multiply elements

6X^2+36X+11=0

a = 6; b = 36; c = +11;
Δ = b2-4ac
Δ = 362-4·6·11
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{258}}{2*6}=\frac{-36-2\sqrt{258}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{258}}{2*6}=\frac{-36+2\sqrt{258}}{12}
$