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x/5x-10=2+2x
We move all terms to the left:
x/5x-10-(2+2x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
x/5x-(2x+2)-10=0
We get rid of parentheses
x/5x-2x-2-10=0
We multiply all the terms by the denominator
x-2x*5x-2*5x-10*5x=0
Wy multiply elements
-10x^2+x-10x-50x=0
We add all the numbers together, and all the variables
-10x^2-59x=0
a = -10; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·(-10)·0
Δ = 3481
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{3481}=59$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*-10}=\frac{0}{-20} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*-10}=\frac{118}{-20} =-5+9/10 $
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