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4x=3/2x+5
We move all terms to the left:
4x-(3/2x+5)=0
Domain of the equation: 2x+5)!=0We get rid of parentheses
x∈R
4x-3/2x-5=0
We multiply all the terms by the denominator
4x*2x-5*2x-3=0
Wy multiply elements
8x^2-10x-3=0
a = 8; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·8·(-3)
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*8}=\frac{-4}{16} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*8}=\frac{24}{16} =1+1/2 $
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