5/12x+23x=37

Solution for 5/12x+23x=37 equation:

5/12x+23x=37

We move all terms to the left:

5/12x+23x-(37)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

23x+5/12x-37=0

We multiply all the terms by the denominator


23x*12x-37*12x+5=0

Wy multiply elements

276x^2-444x+5=0

a = 276; b = -444; c = +5;
Δ = b2-4ac
Δ = -4442-4·276·5
Δ = 191616
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:

$\sqrt{\Delta}=\sqrt{191616}=\sqrt{64*2994}=\sqrt{64}*\sqrt{2994}=8\sqrt{2994}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-444)-8\sqrt{2994}}{2*276}=\frac{444-8\sqrt{2994}}{552}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-444)+8\sqrt{2994}}{2*276}=\frac{444+8\sqrt{2994}}{552}
$