2/3d-14d=-22

Solution for 2/3d-14d=-22 equation:

2/3d-14d=-22

We move all terms to the left:

2/3d-14d-(-22)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R


We add all the numbers together, and all the variables

-14d+2/3d+22=0

We multiply all the terms by the denominator


-14d*3d+22*3d+2=0

Wy multiply elements

-42d^2+66d+2=0

a = -42; b = 66; c = +2;
Δ = b2-4ac
Δ = 662-4·(-42)·2
Δ = 4692
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:

$\sqrt{\Delta}=\sqrt{4692}=\sqrt{4*1173}=\sqrt{4}*\sqrt{1173}=2\sqrt{1173}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1173}}{2*-42}=\frac{-66-2\sqrt{1173}}{-84}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1173}}{2*-42}=\frac{-66+2\sqrt{1173}}{-84}
$