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/7Y=Y+30
We move all terms to the left:
/7Y-(Y+30)=0
Domain of the equation: 7Y!=0We get rid of parentheses
Y!=0/7
Y!=0
Y∈R
/7Y-Y-30=0
We multiply all the terms by the denominator
-Y*7Y-30*7Y+=0
We add all the numbers together, and all the variables
-Y*7Y-30*7Y=0
Wy multiply elements
-7Y^2-210Y=0
a = -7; b = -210; c = 0;
Δ = b2-4ac
Δ = -2102-4·(-7)·0
Δ = 44100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{44100}=210$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-210}{2*-7}=\frac{0}{-14} =0 $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+210}{2*-7}=\frac{420}{-14} =-30 $
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