3x^2+x+1=-5x

Solution for 3x^2+x+1=-5x equation:

3x^2+x+1=-5x

We move all terms to the left:

3x^2+x+1-(-5x)=0

We get rid of parentheses

3x^2+x+5x+1=0

We add all the numbers together, and all the variables

3x^2+6x+1=0

a = 3; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·3·1
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*3}=\frac{-6-2\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*3}=\frac{-6+2\sqrt{6}}{6}
$