3k+7=3/2(5k)

Solution for 3k+7=3/2(5k) equation:

3k+7=3/2(5k)

We move all terms to the left:

3k+7-(3/2(5k))=0


Domain of the equation: 25k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3k-(+3/25k)+7=0

We get rid of parentheses

3k-3/25k+7=0

We multiply all the terms by the denominator


3k*25k+7*25k-3=0

Wy multiply elements

75k^2+175k-3=0

a = 75; b = 175; c = -3;
Δ = b2-4ac
Δ = 1752-4·75·(-3)
Δ = 31525
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31525}=\sqrt{25*1261}=\sqrt{25}*\sqrt{1261}=5\sqrt{1261}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-5\sqrt{1261}}{2*75}=\frac{-175-5\sqrt{1261}}{150}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+5\sqrt{1261}}{2*75}=\frac{-175+5\sqrt{1261}}{150}
$