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9+1/2x=5x-10
We move all terms to the left:
9+1/2x-(5x-10)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-5x+10+9=0
We multiply all the terms by the denominator
-5x*2x+10*2x+9*2x+1=0
Wy multiply elements
-10x^2+20x+18x+1=0
We add all the numbers together, and all the variables
-10x^2+38x+1=0
a = -10; b = 38; c = +1;
Δ = b2-4ac
Δ = 382-4·(-10)·1
Δ = 1484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1484}=\sqrt{4*371}=\sqrt{4}*\sqrt{371}=2\sqrt{371}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{371}}{2*-10}=\frac{-38-2\sqrt{371}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{371}}{2*-10}=\frac{-38+2\sqrt{371}}{-20} $
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