4x+1/2x=175

Solution for 4x+1/2x=175 equation:

4x+1/2x=175

We move all terms to the left:

4x+1/2x-(175)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-175*2x+1=0

Wy multiply elements

8x^2-350x+1=0

a = 8; b = -350; c = +1;
Δ = b2-4ac
Δ = -3502-4·8·1
Δ = 122468
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:

$\sqrt{\Delta}=\sqrt{122468}=\sqrt{4*30617}=\sqrt{4}*\sqrt{30617}=2\sqrt{30617}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30617}}{2*8}=\frac{350-2\sqrt{30617}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30617}}{2*8}=\frac{350+2\sqrt{30617}}{16}
$