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9/10x-x+1=10

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Solution for 9/10x-x+1=10 equation:



9/10x-x+1=10
We move all terms to the left:
9/10x-x+1-(10)=0
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+9/10x-9=0
We multiply all the terms by the denominator
-1x*10x-9*10x+9=0
Wy multiply elements
-10x^2-90x+9=0
a = -10; b = -90; c = +9;
Δ = b2-4ac
Δ = -902-4·(-10)·9
Δ = 8460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}

The end solution:
\sqrt{\Delta}=\sqrt{8460}=\sqrt{36*235}=\sqrt{36}*\sqrt{235}=6\sqrt{235}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{235}}{2*-10}=\frac{90-6\sqrt{235}}{-20}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{235}}{2*-10}=\frac{90+6\sqrt{235}}{-20}

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