4x+2x=-1/2x+10

Solution for 4x+2x=-1/2x+10 equation:

4x+2x=-1/2x+10

We move all terms to the left:

4x+2x-(-1/2x+10)=0


Domain of the equation: 2x+10)!=0

x∈R


We add all the numbers together, and all the variables

6x-(-1/2x+10)=0

We get rid of parentheses

6x+1/2x-10=0

We multiply all the terms by the denominator


6x*2x-10*2x+1=0

Wy multiply elements

12x^2-20x+1=0

a = 12; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·12·1
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{22}}{2*12}=\frac{20-4\sqrt{22}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{22}}{2*12}=\frac{20+4\sqrt{22}}{24}
$