6x^2-14=-8x

Solution for 6x^2-14=-8x equation:

6x^2-14=-8x

We move all terms to the left:

6x^2-14-(-8x)=0

We get rid of parentheses

6x^2+8x-14=0

a = 6; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·6·(-14)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-20}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+20}{2*6}=\frac{12}{12}
=1
$