1/3x+1=4x-10

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Solution for 1/3x+1=4x-10 equation: 



1/3x+1=4x-10

We move all terms to the left:

1/3x+1-(4x-10)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We get rid of parentheses

1/3x-4x+10+1=0

We multiply all the terms by the denominator


-4x*3x+10*3x+1*3x+1=0

Wy multiply elements

-12x^2+30x+3x+1=0

We add all the numbers together, and all the variables

-12x^2+33x+1=0

a = -12; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-12)·1
Δ = 1137
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{-(33)-\sqrt{1137}}{2*-12}=\frac{-33-\sqrt{1137}}{-24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1137}}{2*-12}=\frac{-33+\sqrt{1137}}{-24}
$

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