15x^2-6=-x

Solution for 15x^2-6=-x equation:

15x^2-6=-x

We move all terms to the left:

15x^2-6-(-x)=0

We add all the numbers together, and all the variables

15x^2-(-1x)-6=0

We get rid of parentheses

15x^2+1x-6=0

We add all the numbers together, and all the variables

15x^2+x-6=0

a = 15; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·15·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*15}=\frac{-20}{30}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*15}=\frac{18}{30}
=3/5
$