2d^2-14d+19=0

Solution for 2d^2-14d+19=0 equation:

2d^2-14d+19=0

a = 2; b = -14; c = +19;
Δ = b2-4ac
Δ = -142-4·2·19
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{11}}{2*2}=\frac{14-2\sqrt{11}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{11}}{2*2}=\frac{14+2\sqrt{11}}{4}
$