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

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

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

We move all terms to the left:

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


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


864k^2/1200k^2+(-750k)/1200k^2+(-1400k)/1200k^2+8=0

We multiply all the terms by the denominator


864k^2+(-750k)+(-1400k)+8*1200k^2=0

Wy multiply elements

864k^2+9600k^2+(-750k)+(-1400k)=0

We get rid of parentheses

864k^2+9600k^2-750k-1400k=0

We add all the numbers together, and all the variables

10464k^2-2150k=0

a = 10464; b = -2150; c = 0;
Δ = b2-4ac
Δ = -21502-4·10464·0
Δ = 4622500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4622500}=2150$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2150)-2150}{2*10464}=\frac{0}{20928}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2150)+2150}{2*10464}=\frac{4300}{20928}
=1075/5232
$