4x=1/2x+280

Solution for 4x=1/2x+280 equation:

4x=1/2x+280

We move all terms to the left:

4x-(1/2x+280)=0


Domain of the equation: 2x+280)!=0

x∈R


We get rid of parentheses

4x-1/2x-280=0

We multiply all the terms by the denominator


4x*2x-280*2x-1=0

Wy multiply elements

8x^2-560x-1=0

a = 8; b = -560; c = -1;
Δ = b2-4ac
Δ = -5602-4·8·(-1)
Δ = 313632
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:

$\sqrt{\Delta}=\sqrt{313632}=\sqrt{156816*2}=\sqrt{156816}*\sqrt{2}=396\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-560)-396\sqrt{2}}{2*8}=\frac{560-396\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-560)+396\sqrt{2}}{2*8}=\frac{560+396\sqrt{2}}{16}
$