2x^2+7x-14=-x^2+4x

Solution for 2x^2+7x-14=-x^2+4x equation:

2x^2+7x-14=-x^2+4x

We move all terms to the left:

2x^2+7x-14-(-x^2+4x)=0

We get rid of parentheses

2x^2+x^2-4x+7x-14=0

We add all the numbers together, and all the variables

3x^2+3x-14=0

a = 3; b = 3; c = -14;
Δ = b2-4ac
Δ = 32-4·3·(-14)
Δ = 177
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{177}}{2*3}=\frac{-3-\sqrt{177}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{177}}{2*3}=\frac{-3+\sqrt{177}}{6}
$