5x+1/2x=150

Solution for 5x+1/2x=150 equation:

5x+1/2x=150

We move all terms to the left:

5x+1/2x-(150)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-150*2x+1=0

Wy multiply elements

10x^2-300x+1=0

a = 10; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·10·1
Δ = 89960
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:

$\sqrt{\Delta}=\sqrt{89960}=\sqrt{4*22490}=\sqrt{4}*\sqrt{22490}=2\sqrt{22490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22490}}{2*10}=\frac{300-2\sqrt{22490}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22490}}{2*10}=\frac{300+2\sqrt{22490}}{20}
$