5d+34=-2(1-7d)d

Solution for 5d+34=-2(1-7d)d equation:

5d+34=-2(1-7d)d

We move all terms to the left:

5d+34-(-2(1-7d)d)=0

We add all the numbers together, and all the variables

5d-(-2(-7d+1)d)+34=0


We calculate terms in parentheses: -(-2(-7d+1)d), so:

-2(-7d+1)d

We multiply parentheses

14d^2-2d

Back to the equation:

-(14d^2-2d)


We get rid of parentheses

-14d^2+5d+2d+34=0

We add all the numbers together, and all the variables

-14d^2+7d+34=0

a = -14; b = 7; c = +34;
Δ = b2-4ac
Δ = 72-4·(-14)·34
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{217}}{2*-14}=\frac{-7-3\sqrt{217}}{-28}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{217}}{2*-14}=\frac{-7+3\sqrt{217}}{-28}
$