-1/22x+4+6=-9+42x+1

Solution for -1/22x+4+6=-9+42x+1 equation:

-1/22x+4+6=-9+42x+1

We move all terms to the left:

-1/22x+4+6-(-9+42x+1)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We add all the numbers together, and all the variables

-1/22x-(42x-8)+4+6=0

We add all the numbers together, and all the variables

-1/22x-(42x-8)+10=0

We get rid of parentheses

-1/22x-42x+8+10=0

We multiply all the terms by the denominator


-42x*22x+8*22x+10*22x-1=0

Wy multiply elements

-924x^2+176x+220x-1=0

We add all the numbers together, and all the variables

-924x^2+396x-1=0

a = -924; b = 396; c = -1;
Δ = b2-4ac
Δ = 3962-4·(-924)·(-1)
Δ = 153120
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:

$\sqrt{\Delta}=\sqrt{153120}=\sqrt{16*9570}=\sqrt{16}*\sqrt{9570}=4\sqrt{9570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-4\sqrt{9570}}{2*-924}=\frac{-396-4\sqrt{9570}}{-1848}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+4\sqrt{9570}}{2*-924}=\frac{-396+4\sqrt{9570}}{-1848}
$