/x-4=3x-3.5

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Solution for /x-4=3x-3.5 equation:



/x-4=3x-3.5
We move all terms to the left:
/x-4-(3x-3.5)=0
Domain of the equation: x!=0
x∈R
We get rid of parentheses
/x-3x+3.5-4=0
We multiply all the terms by the denominator
-3x*x+(3.5)*x-4*x+=0
We add all the numbers together, and all the variables
-4x-3x*x+(3.5)*x=0
We multiply parentheses
-4x-3x*x+3.5x=0
Wy multiply elements
-3x^2-4x+3.5x=0
We add all the numbers together, and all the variables
-3x^2-0.5x=0
a = -3; b = -0.5; c = 0;
Δ = b2-4ac
Δ = -0.52-4·(-3)·0
Δ = 0.25
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{-(-0.5)-\sqrt{0.25}}{2*-3}=\frac{0.5-\sqrt{0.25}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.25}}{2*-3}=\frac{0.5+\sqrt{0.25}}{-6} $

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