0=6x^2+x-15

Solution for 0=6x^2+x-15 equation:

0=6x^2+x-15

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-6x^2-x+15=0

We add all the numbers together, and all the variables

-6x^2-1x+15=0

a = -6; b = -1; c = +15;
Δ = b2-4ac
Δ = -12-4·(-6)·15
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*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*-6}=\frac{20}{-12}
=-1+2/3
$