2x^2-28x+97=0

Solution for 2x^2-28x+97=0 equation:

2x^2-28x+97=0

a = 2; b = -28; c = +97;
Δ = b2-4ac
Δ = -282-4·2·97
Δ = 8
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:

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