43x=15-1/3x

Solution for 43x=15-1/3x equation:

43x=15-1/3x

We move all terms to the left:

43x-(15-1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

43x-(-1/3x+15)=0

We get rid of parentheses

43x+1/3x-15=0

We multiply all the terms by the denominator


43x*3x-15*3x+1=0

Wy multiply elements

129x^2-45x+1=0

a = 129; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·129·1
Δ = 1509
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{-(-45)-\sqrt{1509}}{2*129}=\frac{45-\sqrt{1509}}{258}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1509}}{2*129}=\frac{45+\sqrt{1509}}{258}
$