2x^2-16x+34=100

Solution for 2x^2-16x+34=100 equation:

2x^2-16x+34=100

We move all terms to the left:

2x^2-16x+34-(100)=0

We add all the numbers together, and all the variables

2x^2-16x-66=0

a = 2; b = -16; c = -66;
Δ = b2-4ac
Δ = -162-4·2·(-66)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-28}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+28}{2*2}=\frac{44}{4}
=11
$