4x^2-28x+46=0

Solution for 4x^2-28x+46=0 equation:

4x^2-28x+46=0

a = 4; b = -28; c = +46;
Δ = b2-4ac
Δ = -282-4·4·46
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{3}}{2*4}=\frac{28-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{3}}{2*4}=\frac{28+4\sqrt{3}}{8}
$