12/5x+x=374

Solution for 12/5x+x=374 equation:

12/5x+x=374

We move all terms to the left:

12/5x+x-(374)=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-374=0

We multiply all the terms by the denominator


x*5x-374*5x+12=0

Wy multiply elements

5x^2-1870x+12=0

a = 5; b = -1870; c = +12;
Δ = b2-4ac
Δ = -18702-4·5·12
Δ = 3496660
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:

$\sqrt{\Delta}=\sqrt{3496660}=\sqrt{4*874165}=\sqrt{4}*\sqrt{874165}=2\sqrt{874165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1870)-2\sqrt{874165}}{2*5}=\frac{1870-2\sqrt{874165}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1870)+2\sqrt{874165}}{2*5}=\frac{1870+2\sqrt{874165}}{10}
$