7/10k-2=2/5k+1

Solution for 7/10k-2=2/5k+1 equation:

7/10k-2=2/5k+1

We move all terms to the left:

7/10k-2-(2/5k+1)=0


Domain of the equation: 10k!=0

k!=0/10

k!=0

k∈R



Domain of the equation: 5k+1)!=0

k∈R


We get rid of parentheses

7/10k-2/5k-1-2=0

We calculate fractions


35k/50k^2+(-20k)/50k^2-1-2=0

We add all the numbers together, and all the variables

35k/50k^2+(-20k)/50k^2-3=0

We multiply all the terms by the denominator


35k+(-20k)-3*50k^2=0

Wy multiply elements

-150k^2+35k+(-20k)=0

We get rid of parentheses

-150k^2+35k-20k=0

We add all the numbers together, and all the variables

-150k^2+15k=0

a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-150}=\frac{-30}{-300}
=1/10
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300}
=0
$