9d(2d+7)=11(d+14)

Solution for 9d(2d+7)=11(d+14) equation:

9d(2d+7)=11(d+14)

We move all terms to the left:

9d(2d+7)-(11(d+14))=0

We multiply parentheses

18d^2+63d-(11(d+14))=0


We calculate terms in parentheses: -(11(d+14)), so:

11(d+14)

We multiply parentheses

11d+154

Back to the equation:

-(11d+154)


We get rid of parentheses

18d^2+63d-11d-154=0

We add all the numbers together, and all the variables

18d^2+52d-154=0

a = 18; b = 52; c = -154;
Δ = b2-4ac
Δ = 522-4·18·(-154)
Δ = 13792
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:

$\sqrt{\Delta}=\sqrt{13792}=\sqrt{16*862}=\sqrt{16}*\sqrt{862}=4\sqrt{862}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{862}}{2*18}=\frac{-52-4\sqrt{862}}{36}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{862}}{2*18}=\frac{-52+4\sqrt{862}}{36}
$