7x^2=-14x-5

Solution for 7x^2=-14x-5 equation:

7x^2=-14x-5

We move all terms to the left:

7x^2-(-14x-5)=0

We get rid of parentheses

7x^2+14x+5=0

a = 7; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·7·5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{14}}{2*7}=\frac{-14-2\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{14}}{2*7}=\frac{-14+2\sqrt{14}}{14}
$