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2/5x+1=20-3/2x
We move all terms to the left:
2/5x+1-(20-3/2x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/5x-(-3/2x+20)+1=0
We get rid of parentheses
2/5x+3/2x-20+1=0
We calculate fractions
4x/10x^2+15x/10x^2-20+1=0
We add all the numbers together, and all the variables
4x/10x^2+15x/10x^2-19=0
We multiply all the terms by the denominator
4x+15x-19*10x^2=0
We add all the numbers together, and all the variables
19x-19*10x^2=0
Wy multiply elements
-190x^2+19x=0
a = -190; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-190)·0
Δ = 361
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{361}=19x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-190}=\frac{-38}{-380} =1/10x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-190}=\frac{0}{-380} =0
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