1/2x+7x+24=0

Solution for 1/2x+7x+24=0 equation:

1/2x+7x+24=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7x+1/2x+24=0

We multiply all the terms by the denominator


7x*2x+24*2x+1=0

Wy multiply elements

14x^2+48x+1=0

a = 14; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·14·1
Δ = 2248
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:

$\sqrt{\Delta}=\sqrt{2248}=\sqrt{4*562}=\sqrt{4}*\sqrt{562}=2\sqrt{562}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{562}}{2*14}=\frac{-48-2\sqrt{562}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{562}}{2*14}=\frac{-48+2\sqrt{562}}{28}
$