x^2=-(6x+7)

Solution for x^2=-(6x+7) equation:

x^2=-(6x+7)

We move all terms to the left:

x^2-(-(6x+7))=0


We calculate terms in parentheses: -(-(6x+7)), so:

-(6x+7)

We get rid of parentheses

-6x-7

Back to the equation:

-(-6x-7)


We get rid of parentheses

x^2+6x+7=0

a = 1; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·1·7
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2}}{2*1}=\frac{-6-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2}}{2*1}=\frac{-6+2\sqrt{2}}{2}
$