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v-9/10v+6=9
We move all terms to the left:
v-9/10v+6-(9)=0
Domain of the equation: 10v!=0We add all the numbers together, and all the variables
v!=0/10
v!=0
v∈R
v-9/10v-3=0
We multiply all the terms by the denominator
v*10v-3*10v-9=0
Wy multiply elements
10v^2-30v-9=0
a = 10; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·10·(-9)
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:v_{1}=\frac{-b-\sqrt{\Delta}}{2a}v_{2}=\frac{-b+\sqrt{\Delta}}{2a}
The end solution:
\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{35}}{2*10}=\frac{30-6\sqrt{35}}{20}v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{35}}{2*10}=\frac{30+6\sqrt{35}}{20}
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