X^2+6x=-11/14

Solution for X^2+6x=-11/14 equation:

X^2+6X=-11/14

We move all terms to the left:

X^2+6X-(-11/14)=0

We get rid of parentheses

X^2+6X+11/14=0

We multiply all the terms by the denominator


X^2*14+6X*14+11=0

Wy multiply elements

14X^2+84X+11=0

a = 14; b = 84; c = +11;
Δ = b2-4ac
Δ = 842-4·14·11
Δ = 6440
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:

$\sqrt{\Delta}=\sqrt{6440}=\sqrt{4*1610}=\sqrt{4}*\sqrt{1610}=2\sqrt{1610}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-2\sqrt{1610}}{2*14}=\frac{-84-2\sqrt{1610}}{28}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+2\sqrt{1610}}{2*14}=\frac{-84+2\sqrt{1610}}{28}
$