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3.1+7.5x-5.1=-x-2+17/2x
We move all terms to the left:
3.1+7.5x-5.1-(-x-2+17/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
7.5x-(-1x+17/2x-2)+3.1-5.1=0
We add all the numbers together, and all the variables
7.5x-(-1x+17/2x-2)-2=0
We get rid of parentheses
7.5x+1x-17/2x+2-2=0
We multiply all the terms by the denominator
(7.5x)*2x+1x*2x+2*2x-2*2x-17=0
We add all the numbers together, and all the variables
(+7.5x)*2x+1x*2x+2*2x-2*2x-17=0
We multiply parentheses
14x^2+1x*2x+2*2x-2*2x-17=0
Wy multiply elements
14x^2+2x^2+4x-4x-17=0
We add all the numbers together, and all the variables
16x^2-17=0
a = 16; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·16·(-17)
Δ = 1088
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{17}}{2*16}=\frac{0-8\sqrt{17}}{32} =-\frac{8\sqrt{17}}{32} =-\frac{\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{17}}{2*16}=\frac{0+8\sqrt{17}}{32} =\frac{8\sqrt{17}}{32} =\frac{\sqrt{17}}{4} $
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