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((7)/(10)a+5)=(7)/(8)a-10

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Solution for ((7)/(10)a+5)=(7)/(8)a-10 equation:



((7)/(10)a+5)=(7)/(8)a-10
We move all terms to the left:
((7)/(10)a+5)-((7)/(8)a-10)=0
Domain of the equation: 10a+5)!=0
a∈R
Domain of the equation: 8a-10)!=0
a∈R
We get rid of parentheses
7/10a-7/8a+5+10=0
We calculate fractions
56a/80a^2+(-70a)/80a^2+5+10=0
We add all the numbers together, and all the variables
56a/80a^2+(-70a)/80a^2+15=0
We multiply all the terms by the denominator
56a+(-70a)+15*80a^2=0
Wy multiply elements
1200a^2+56a+(-70a)=0
We get rid of parentheses
1200a^2+56a-70a=0
We add all the numbers together, and all the variables
1200a^2-14a=0
a = 1200; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·1200·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
a_{1}=\frac{-b-\sqrt{\Delta}}{2a}
a_{2}=\frac{-b+\sqrt{\Delta}}{2a}

\sqrt{\Delta}=\sqrt{196}=14
a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*1200}=\frac{0}{2400} =0
a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*1200}=\frac{28}{2400} =7/600

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