65=2(d+1)5d

Solution for 65=2(d+1)5d equation:

65=2(d+1)5d

We move all terms to the left:

65-(2(d+1)5d)=0


We calculate terms in parentheses: -(2(d+1)5d), so:

2(d+1)5d

We multiply parentheses

10d^2+10d

Back to the equation:

-(10d^2+10d)


We get rid of parentheses

-10d^2-10d+65=0

a = -10; b = -10; c = +65;
Δ = b2-4ac
Δ = -102-4·(-10)·65
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30\sqrt{3}}{2*-10}=\frac{10-30\sqrt{3}}{-20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30\sqrt{3}}{2*-10}=\frac{10+30\sqrt{3}}{-20}
$