15=1/22x+3x+10

Solution for 15=1/22x+3x+10 equation:

15=1/22x+3x+10

We move all terms to the left:

15-(1/22x+3x+10)=0


Domain of the equation: 22x+3x+10)!=0

x∈R


We add all the numbers together, and all the variables

-(3x+1/22x+10)+15=0

We get rid of parentheses

-3x-1/22x-10+15=0

We multiply all the terms by the denominator


-3x*22x-10*22x+15*22x-1=0

Wy multiply elements

-66x^2-220x+330x-1=0

We add all the numbers together, and all the variables

-66x^2+110x-1=0

a = -66; b = 110; c = -1;
Δ = b2-4ac
Δ = 1102-4·(-66)·(-1)
Δ = 11836
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:

$\sqrt{\Delta}=\sqrt{11836}=\sqrt{4*2959}=\sqrt{4}*\sqrt{2959}=2\sqrt{2959}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{2959}}{2*-66}=\frac{-110-2\sqrt{2959}}{-132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{2959}}{2*-66}=\frac{-110+2\sqrt{2959}}{-132}
$