15x^2-x-2=2x-1

Solution for 15x^2-x-2=2x-1 equation:

15x^2-x-2=2x-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2-3x-1=0

a = 15; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·15·(-1)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{69}}{2*15}=\frac{3-\sqrt{69}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*15}=\frac{3+\sqrt{69}}{30}
$