7x^2+35x=-21

Solution for 7x^2+35x=-21 equation:

7x^2+35x=-21

We move all terms to the left:

7x^2+35x-(-21)=0

We add all the numbers together, and all the variables

7x^2+35x+21=0

a = 7; b = 35; c = +21;
Δ = b2-4ac
Δ = 352-4·7·21
Δ = 637
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:

$\sqrt{\Delta}=\sqrt{637}=\sqrt{49*13}=\sqrt{49}*\sqrt{13}=7\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{13}}{2*7}=\frac{-35-7\sqrt{13}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{13}}{2*7}=\frac{-35+7\sqrt{13}}{14}
$