7x^2=-35-35x

Solution for 7x^2=-35-35x equation:

7x^2=-35-35x

We move all terms to the left:

7x^2-(-35-35x)=0

We add all the numbers together, and all the variables

7x^2-(-35x-35)=0

We get rid of parentheses

7x^2+35x+35=0

a = 7; b = 35; c = +35;
Δ = b2-4ac
Δ = 352-4·7·35
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{5}}{2*7}=\frac{-35-7\sqrt{5}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{5}}{2*7}=\frac{-35+7\sqrt{5}}{14}
$