45x+5/6x=50

Solution for 45x+5/6x=50 equation:

45x+5/6x=50

We move all terms to the left:

45x+5/6x-(50)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


45x*6x-50*6x+5=0

Wy multiply elements

270x^2-300x+5=0

a = 270; b = -300; c = +5;
Δ = b2-4ac
Δ = -3002-4·270·5
Δ = 84600
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:

$\sqrt{\Delta}=\sqrt{84600}=\sqrt{900*94}=\sqrt{900}*\sqrt{94}=30\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-30\sqrt{94}}{2*270}=\frac{300-30\sqrt{94}}{540}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+30\sqrt{94}}{2*270}=\frac{300+30\sqrt{94}}{540}
$