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X+3=5/2X+1
We move all terms to the left:
X+3-(5/2X+1)=0
Domain of the equation: 2X+1)!=0We get rid of parentheses
X∈R
X-5/2X-1+3=0
We multiply all the terms by the denominator
X*2X-1*2X+3*2X-5=0
Wy multiply elements
2X^2-2X+6X-5=0
We add all the numbers together, and all the variables
2X^2+4X-5=0
a = 2; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·2·(-5)
Δ = 56
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{14}}{2*2}=\frac{-4-2\sqrt{14}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{14}}{2*2}=\frac{-4+2\sqrt{14}}{4} $
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