3x^2-10x-14=-x^2

Solution for 3x^2-10x-14=-x^2 equation:

3x^2-10x-14=-x^2

We move all terms to the left:

3x^2-10x-14-(-x^2)=0

We get rid of parentheses

3x^2+x^2-10x-14=0

We add all the numbers together, and all the variables

4x^2-10x-14=0

a = 4; b = -10; c = -14;
Δ = b2-4ac
Δ = -102-4·4·(-14)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18}{2*4}=\frac{28}{8}
=3+1/2
$