5x^2+1=-13x-5

Solution for 5x^2+1=-13x-5 equation:

5x^2+1=-13x-5

We move all terms to the left:

5x^2+1-(-13x-5)=0

We get rid of parentheses

5x^2+13x+5+1=0

We add all the numbers together, and all the variables

5x^2+13x+6=0

a = 5; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·5·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-7}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*5}=\frac{-6}{10}
=-3/5
$