-2x^2+22x-14=34

Solution for -2x^2+22x-14=34 equation:

-2x^2+22x-14=34

We move all terms to the left:

-2x^2+22x-14-(34)=0

We add all the numbers together, and all the variables

-2x^2+22x-48=0

a = -2; b = 22; c = -48;
Δ = b2-4ac
Δ = 222-4·(-2)·(-48)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10}{2*-2}=\frac{-12}{-4}
=+3
$