5x^2-x-30=2x^2-x

Solution for 5x^2-x-30=2x^2-x equation:

5x^2-x-30=2x^2-x

We move all terms to the left:

5x^2-x-30-(2x^2-x)=0

We add all the numbers together, and all the variables

5x^2-1x-(2x^2-x)-30=0

We get rid of parentheses

5x^2-2x^2-1x+x-30=0

We add all the numbers together, and all the variables

3x^2-30=0

a = 3; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·3·(-30)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*3}=\frac{0-6\sqrt{10}}{6}
=-\frac{6\sqrt{10}}{6}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*3}=\frac{0+6\sqrt{10}}{6}
=\frac{6\sqrt{10}}{6}
=\sqrt{10}
$