4/5k-3=3/10k+7

Solution for 4/5k-3=3/10k+7 equation:

4/5k-3=3/10k+7

We move all terms to the left:

4/5k-3-(3/10k+7)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 10k+7)!=0

k∈R


We get rid of parentheses

4/5k-3/10k-7-3=0

We calculate fractions


40k/50k^2+(-15k)/50k^2-7-3=0

We add all the numbers together, and all the variables

40k/50k^2+(-15k)/50k^2-10=0

We multiply all the terms by the denominator


40k+(-15k)-10*50k^2=0

Wy multiply elements

-500k^2+40k+(-15k)=0

We get rid of parentheses

-500k^2+40k-15k=0

We add all the numbers together, and all the variables

-500k^2+25k=0

a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-500}=\frac{-50}{-1000}
=1/20
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-500}=\frac{0}{-1000}
=0
$