14x^2-44x+15=0

Solution for 14x^2-44x+15=0 equation:

14x^2-44x+15=0

a = 14; b = -44; c = +15;
Δ = b2-4ac
Δ = -442-4·14·15
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{274}}{2*14}=\frac{44-2\sqrt{274}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{274}}{2*14}=\frac{44+2\sqrt{274}}{28}
$