1/22x+4x=10

Solution for 1/22x+4x=10 equation:

1/22x+4x=10

We move all terms to the left:

1/22x+4x-(10)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/22x-10=0

We multiply all the terms by the denominator


4x*22x-10*22x+1=0

Wy multiply elements

88x^2-220x+1=0

a = 88; b = -220; c = +1;
Δ = b2-4ac
Δ = -2202-4·88·1
Δ = 48048
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:

$\sqrt{\Delta}=\sqrt{48048}=\sqrt{16*3003}=\sqrt{16}*\sqrt{3003}=4\sqrt{3003}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{3003}}{2*88}=\frac{220-4\sqrt{3003}}{176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{3003}}{2*88}=\frac{220+4\sqrt{3003}}{176}
$