2x2+14x-4=-x2+3x

Solution for 2x2+14x-4=-x2+3x equation:

2x^2+14x-4=-x2+3x

We move all terms to the left:

2x^2+14x-4-(-x2+3x)=0

We add all the numbers together, and all the variables

2x^2-(-1x^2+3x)+14x-4=0

We get rid of parentheses

2x^2+1x^2-3x+14x-4=0

We add all the numbers together, and all the variables

3x^2+11x-4=0

a = 3; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·3·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*3}=\frac{2}{6}
=1/3
$