10x+2/5x=156

Solution for 10x+2/5x=156 equation:

10x+2/5x=156

We move all terms to the left:

10x+2/5x-(156)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


10x*5x-156*5x+2=0

Wy multiply elements

50x^2-780x+2=0

a = 50; b = -780; c = +2;
Δ = b2-4ac
Δ = -7802-4·50·2
Δ = 608000
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:

$\sqrt{\Delta}=\sqrt{608000}=\sqrt{6400*95}=\sqrt{6400}*\sqrt{95}=80\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-780)-80\sqrt{95}}{2*50}=\frac{780-80\sqrt{95}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-780)+80\sqrt{95}}{2*50}=\frac{780+80\sqrt{95}}{100}
$