51/5x+2/3x=37

Solution for 51/5x+2/3x=37 equation:

51/5x+2/3x=37

We move all terms to the left:

51/5x+2/3x-(37)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


153x/15x^2+10x/15x^2-37=0

We multiply all the terms by the denominator


153x+10x-37*15x^2=0

We add all the numbers together, and all the variables

163x-37*15x^2=0

Wy multiply elements

-555x^2+163x=0

a = -555; b = 163; c = 0;
Δ = b2-4ac
Δ = 1632-4·(-555)·0
Δ = 26569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26569}=163$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(163)-163}{2*-555}=\frac{-326}{-1110}
=163/555
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(163)+163}{2*-555}=\frac{0}{-1110}
=0
$