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3x+1=31/4x
We move all terms to the left:
3x+1-(31/4x)=0
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3x-(+31/4x)+1=0
We get rid of parentheses
3x-31/4x+1=0
We multiply all the terms by the denominator
3x*4x+1*4x-31=0
Wy multiply elements
12x^2+4x-31=0
a = 12; b = 4; c = -31;
Δ = b2-4ac
Δ = 42-4·12·(-31)
Δ = 1504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{94}}{2*12}=\frac{-4-4\sqrt{94}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{94}}{2*12}=\frac{-4+4\sqrt{94}}{24} $
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