2/10x+5x=11

Solution for 2/10x+5x=11 equation:

2/10x+5x=11

We move all terms to the left:

2/10x+5x-(11)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

5x+2/10x-11=0

We multiply all the terms by the denominator


5x*10x-11*10x+2=0

Wy multiply elements

50x^2-110x+2=0

a = 50; b = -110; c = +2;
Δ = b2-4ac
Δ = -1102-4·50·2
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-30\sqrt{13}}{2*50}=\frac{110-30\sqrt{13}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+30\sqrt{13}}{2*50}=\frac{110+30\sqrt{13}}{100}
$