4x^2-26x+28=0

Solution for 4x^2-26x+28=0 equation:

4x^2-26x+28=0

a = 4; b = -26; c = +28;
Δ = b2-4ac
Δ = -262-4·4·28
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{57}}{2*4}=\frac{26-2\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{57}}{2*4}=\frac{26+2\sqrt{57}}{8}
$