2d^2-12d-7=0

Solution for 2d^2-12d-7=0 equation:

2d^2-12d-7=0

a = 2; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·2·(-7)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{2}}{2*2}=\frac{12-10\sqrt{2}}{4}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{2}}{2*2}=\frac{12+10\sqrt{2}}{4}
$