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4/5z+2=7/10z
We move all terms to the left:
4/5z+2-(7/10z)=0
Domain of the equation: 5z!=0
z!=0/5
z!=0
z∈R
Domain of the equation: 10z)!=0We add all the numbers together, and all the variables
z!=0/1
z!=0
z∈R
4/5z-(+7/10z)+2=0
We get rid of parentheses
4/5z-7/10z+2=0
We calculate fractions
40z/50z^2+(-35z)/50z^2+2=0
We multiply all the terms by the denominator
40z+(-35z)+2*50z^2=0
Wy multiply elements
100z^2+40z+(-35z)=0
We get rid of parentheses
100z^2+40z-35z=0
We add all the numbers together, and all the variables
100z^2+5z=0
a = 100; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·100·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*100}=\frac{-10}{200} =-1/20 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*100}=\frac{0}{200} =0 $
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