2/5d+6=2d-4

Solution for 2/5d+6=2d-4 equation:

2/5d+6=2d-4

We move all terms to the left:

2/5d+6-(2d-4)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We get rid of parentheses

2/5d-2d+4+6=0

We multiply all the terms by the denominator


-2d*5d+4*5d+6*5d+2=0

Wy multiply elements

-10d^2+20d+30d+2=0

We add all the numbers together, and all the variables

-10d^2+50d+2=0

a = -10; b = 50; c = +2;
Δ = b2-4ac
Δ = 502-4·(-10)·2
Δ = 2580
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:

$\sqrt{\Delta}=\sqrt{2580}=\sqrt{4*645}=\sqrt{4}*\sqrt{645}=2\sqrt{645}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{645}}{2*-10}=\frac{-50-2\sqrt{645}}{-20}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{645}}{2*-10}=\frac{-50+2\sqrt{645}}{-20}
$