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

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

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

We move all terms to the left:

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

We multiply parentheses

7d^2-14d-(5(d+2))=0


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

5(d+2)

We multiply parentheses

5d+10

Back to the equation:

-(5d+10)


We get rid of parentheses

7d^2-14d-5d-10=0

We add all the numbers together, and all the variables

7d^2-19d-10=0

a = 7; b = -19; c = -10;
Δ = b2-4ac
Δ = -192-4·7·(-10)
Δ = 641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{641}}{2*7}=\frac{19-\sqrt{641}}{14}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{641}}{2*7}=\frac{19+\sqrt{641}}{14}
$