X^2+7x+7=66-x

Solution for X^2+7x+7=66-x equation:

X^2+7X+7=66-X

We move all terms to the left:

X^2+7X+7-(66-X)=0

We add all the numbers together, and all the variables

X^2+7X-(-1X+66)+7=0

We get rid of parentheses

X^2+7X+1X-66+7=0

We add all the numbers together, and all the variables

X^2+8X-59=0

a = 1; b = 8; c = -59;
Δ = b2-4ac
Δ = 82-4·1·(-59)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10\sqrt{3}}{2*1}=\frac{-8-10\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10\sqrt{3}}{2*1}=\frac{-8+10\sqrt{3}}{2}
$