4x^2-x=-13x

Solution for 4x^2-x=-13x equation:

4x^2-x=-13x

We move all terms to the left:

4x^2-x-(-13x)=0

We add all the numbers together, and all the variables

4x^2-1x-(-13x)=0

We get rid of parentheses

4x^2-1x+13x=0

We add all the numbers together, and all the variables

4x^2+12x=0

a = 4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·4·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*4}=\frac{0}{8}
=0
$