(1/5)x+13+x=1-9x+22

Solution for (1/5)x+13+x=1-9x+22 equation:

(1/5)x+13+x=1-9x+22

We move all terms to the left:

(1/5)x+13+x-(1-9x+22)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/5)x+x-(-9x+23)+13=0

We add all the numbers together, and all the variables

x+(+1/5)x-(-9x+23)+13=0

We multiply parentheses

x^2+x-(-9x+23)+13=0

We get rid of parentheses

x^2+x+9x-23+13=0

We add all the numbers together, and all the variables

x^2+10x-10=0

a = 1; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·1·(-10)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*1}=\frac{-10-2\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*1}=\frac{-10+2\sqrt{35}}{2}
$