4x^2-2x+16=46

Solution for 4x^2-2x+16=46 equation:

4x^2-2x+16=46

We move all terms to the left:

4x^2-2x+16-(46)=0

We add all the numbers together, and all the variables

4x^2-2x-30=0

a = 4; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·4·(-30)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*4}=\frac{24}{8}
=3
$