4(d+7)d=2

Solution for 4(d+7)d=2 equation:

4(d+7)d=2

We move all terms to the left:

4(d+7)d-(2)=0

We multiply parentheses

4d^2+28d-2=0

a = 4; b = 28; c = -2;
Δ = b2-4ac
Δ = 282-4·4·(-2)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*4}=\frac{-28-4\sqrt{51}}{8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*4}=\frac{-28+4\sqrt{51}}{8}
$