-9/5k-1/8=-5-6/7k

Solution for -9/5k-1/8=-5-6/7k equation:

-9/5k-1/8=-5-6/7k

We move all terms to the left:

-9/5k-1/8-(-5-6/7k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-9/5k-(-6/7k-5)-1/8=0

We get rid of parentheses

-9/5k+6/7k+5-1/8=0

We calculate fractions


(-245k^2)/2240k^2+(-4032k)/2240k^2+1920k/2240k^2+5=0

We multiply all the terms by the denominator


(-245k^2)+(-4032k)+1920k+5*2240k^2=0

We add all the numbers together, and all the variables

(-245k^2)+1920k+(-4032k)+5*2240k^2=0

Wy multiply elements

(-245k^2)+11200k^2+1920k+(-4032k)=0

We get rid of parentheses

-245k^2+11200k^2+1920k-4032k=0

We add all the numbers together, and all the variables

10955k^2-2112k=0

a = 10955; b = -2112; c = 0;
Δ = b2-4ac
Δ = -21122-4·10955·0
Δ = 4460544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4460544}=2112$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2112)-2112}{2*10955}=\frac{0}{21910}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2112)+2112}{2*10955}=\frac{4224}{21910}
=2112/10955
$