2x^2+x=5x^2-7

Solution for 2x^2+x=5x^2-7 equation:

2x^2+x=5x^2-7

We move all terms to the left:

2x^2+x-(5x^2-7)=0

We get rid of parentheses

2x^2-5x^2+x+7=0

We add all the numbers together, and all the variables

-3x^2+x+7=0

a = -3; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-3)·7
Δ = 85
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{-(1)-\sqrt{85}}{2*-3}=\frac{-1-\sqrt{85}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{85}}{2*-3}=\frac{-1+\sqrt{85}}{-6}
$