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3x=1/2x+147.5
We move all terms to the left:
3x-(1/2x+147.5)=0
Domain of the equation: 2x+147.5)!=0We get rid of parentheses
x∈R
3x-1/2x-147.5=0
We multiply all the terms by the denominator
3x*2x-(147.5)*2x-1=0
We multiply parentheses
3x*2x-295x-1=0
Wy multiply elements
6x^2-295x-1=0
a = 6; b = -295; c = -1;
Δ = b2-4ac
Δ = -2952-4·6·(-1)
Δ = 87049
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-295)-\sqrt{87049}}{2*6}=\frac{295-\sqrt{87049}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-295)+\sqrt{87049}}{2*6}=\frac{295+\sqrt{87049}}{12} $
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