-1/2k+10=-10+4/5k

Solution for -1/2k+10=-10+4/5k equation:

-1/2k+10=-10+4/5k

We move all terms to the left:

-1/2k+10-(-10+4/5k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-1/2k-(4/5k-10)+10=0

We get rid of parentheses

-1/2k-4/5k+10+10=0

We calculate fractions


(-5k)/10k^2+(-8k)/10k^2+10+10=0

We add all the numbers together, and all the variables

(-5k)/10k^2+(-8k)/10k^2+20=0

We multiply all the terms by the denominator


(-5k)+(-8k)+20*10k^2=0

Wy multiply elements

200k^2+(-5k)+(-8k)=0

We get rid of parentheses

200k^2-5k-8k=0

We add all the numbers together, and all the variables

200k^2-13k=0

a = 200; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·200·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*200}=\frac{0}{400}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*200}=\frac{26}{400}
=13/200
$