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X/2X-11=7X+19
We move all terms to the left:
X/2X-11-(7X+19)=0
Domain of the equation: 2X!=0We get rid of parentheses
X!=0/2
X!=0
X∈R
X/2X-7X-19-11=0
We multiply all the terms by the denominator
X-7X*2X-19*2X-11*2X=0
Wy multiply elements
-14X^2+X-38X-22X=0
We add all the numbers together, and all the variables
-14X^2-59X=0
a = -14; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·(-14)·0
Δ = 3481
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{3481}=59$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*-14}=\frac{0}{-28} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*-14}=\frac{118}{-28} =-4+3/14 $
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