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-8/7k+4/9=-7+2/5k
We move all terms to the left:
-8/7k+4/9-(-7+2/5k)=0
Domain of the equation: 7k!=0
k!=0/7
k!=0
k∈R
Domain of the equation: 5k)!=0We add all the numbers together, and all the variables
k!=0/1
k!=0
k∈R
-8/7k-(2/5k-7)+4/9=0
We get rid of parentheses
-8/7k-2/5k+7+4/9=0
We calculate fractions
700k^2/2835k^2+(-3240k)/2835k^2+(-1134k)/2835k^2+7=0
We multiply all the terms by the denominator
700k^2+(-3240k)+(-1134k)+7*2835k^2=0
Wy multiply elements
700k^2+19845k^2+(-3240k)+(-1134k)=0
We get rid of parentheses
700k^2+19845k^2-3240k-1134k=0
We add all the numbers together, and all the variables
20545k^2-4374k=0
a = 20545; b = -4374; c = 0;
Δ = b2-4ac
Δ = -43742-4·20545·0
Δ = 19131876
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{19131876}=4374$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4374)-4374}{2*20545}=\frac{0}{41090} =0 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4374)+4374}{2*20545}=\frac{8748}{41090} =4374/20545 $
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