4/5k+6/7=3-3/8k

Solution for 4/5k+6/7=3-3/8k equation:

4/5k+6/7=3-3/8k

We move all terms to the left:

4/5k+6/7-(3-3/8k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 8k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

4/5k-(-3/8k+3)+6/7=0

We get rid of parentheses

4/5k+3/8k-3+6/7=0

We calculate fractions


1920k^2/1960k^2+1568k/1960k^2+735k/1960k^2-3=0

We multiply all the terms by the denominator


1920k^2+1568k+735k-3*1960k^2=0

We add all the numbers together, and all the variables

1920k^2+2303k-3*1960k^2=0

Wy multiply elements

1920k^2-5880k^2+2303k=0

We add all the numbers together, and all the variables

-3960k^2+2303k=0

a = -3960; b = 2303; c = 0;
Δ = b2-4ac
Δ = 23032-4·(-3960)·0
Δ = 5303809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5303809}=2303$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2303)-2303}{2*-3960}=\frac{-4606}{-7920}
=2303/3960
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2303)+2303}{2*-3960}=\frac{0}{-7920}
=0
$