0.5(7d+4)=7-1/5d

Solution for 0.5(7d+4)=7-1/5d equation:

0.5(7d+4)=7-1/5d

We move all terms to the left:

0.5(7d+4)-(7-1/5d)=0


Domain of the equation: 5d)!=0

d!=0/1

d!=0

d∈R


We add all the numbers together, and all the variables

0.5(7d+4)-(-1/5d+7)=0

We multiply parentheses

3.5d-(-1/5d+7)+2=0

We get rid of parentheses

3.5d+1/5d-7+2=0

We multiply all the terms by the denominator


(3.5d)*5d-7*5d+2*5d+1=0

We add all the numbers together, and all the variables

(+3.5d)*5d-7*5d+2*5d+1=0

We multiply parentheses

15d^2-7*5d+2*5d+1=0

Wy multiply elements

15d^2-35d+10d+1=0

We add all the numbers together, and all the variables

15d^2-25d+1=0

a = 15; b = -25; c = +1;
Δ = b2-4ac
Δ = -252-4·15·1
Δ = 565
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{-(-25)-\sqrt{565}}{2*15}=\frac{25-\sqrt{565}}{30}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{565}}{2*15}=\frac{25+\sqrt{565}}{30}
$