4x+10=3/3x

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Solution for 4x+10=3/3x equation:



4x+10=3/3x
We move all terms to the left:
4x+10-(3/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
4x-(+3/3x)+10=0
We get rid of parentheses
4x-3/3x+10=0
We multiply all the terms by the denominator
4x*3x+10*3x-3=0
Wy multiply elements
12x^2+30x-3=0
a = 12; b = 30; c = -3;
Δ = b2-4ac
Δ = 302-4·12·(-3)
Δ = 1044
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:
$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{29}}{2*12}=\frac{-30-6\sqrt{29}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{29}}{2*12}=\frac{-30+6\sqrt{29}}{24} $

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