7(d2)=5(d+2)

Solution for 7(d2)=5(d+2) equation:

7(d2)=5(d+2)

We move all terms to the left:

7(d2)-(5(d+2))=0

We add all the numbers together, and all the variables

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

a = 7; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·7·(-10)
Δ = 305
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{-(-5)-\sqrt{305}}{2*7}=\frac{5-\sqrt{305}}{14}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{305}}{2*7}=\frac{5+\sqrt{305}}{14}
$