x+(1)/(5)x=12

Solution for x+(1)/(5)x=12 equation:

x+(1)/(5)x=12

We move all terms to the left:

x+(1)/(5)x-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-12*5x+1=0

Wy multiply elements

5x^2-60x+1=0

a = 5; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·5·1
Δ = 3580
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:

$\sqrt{\Delta}=\sqrt{3580}=\sqrt{4*895}=\sqrt{4}*\sqrt{895}=2\sqrt{895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{895}}{2*5}=\frac{60-2\sqrt{895}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{895}}{2*5}=\frac{60+2\sqrt{895}}{10}
$