12/5x+x=102

Solution for 12/5x+x=102 equation:

12/5x+x=102

We move all terms to the left:

12/5x+x-(102)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+12/5x-102=0

We multiply all the terms by the denominator


x*5x-102*5x+12=0

Wy multiply elements

5x^2-510x+12=0

a = 5; b = -510; c = +12;
Δ = b2-4ac
Δ = -5102-4·5·12
Δ = 259860
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:

$\sqrt{\Delta}=\sqrt{259860}=\sqrt{4*64965}=\sqrt{4}*\sqrt{64965}=2\sqrt{64965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{64965}}{2*5}=\frac{510-2\sqrt{64965}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{64965}}{2*5}=\frac{510+2\sqrt{64965}}{10}
$