a-5=1/10a+4

Solution for a-5=1/10a+4 equation:

a-5=1/10a+4

We move all terms to the left:

a-5-(1/10a+4)=0


Domain of the equation: 10a+4)!=0

a∈R


We get rid of parentheses

a-1/10a-4-5=0

We multiply all the terms by the denominator


a*10a-4*10a-5*10a-1=0

Wy multiply elements

10a^2-40a-50a-1=0

We add all the numbers together, and all the variables

10a^2-90a-1=0

a = 10; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·10·(-1)
Δ = 8140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2035}}{2*10}=\frac{90-2\sqrt{2035}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2035}}{2*10}=\frac{90+2\sqrt{2035}}{20}
$