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

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

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

We move all terms to the left:

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


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

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-30a^2-50a-1=0

a = -30; b = -50; c = -1;
Δ = b2-4ac
Δ = -502-4·(-30)·(-1)
Δ = 2380
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:

$\sqrt{\Delta}=\sqrt{2380}=\sqrt{4*595}=\sqrt{4}*\sqrt{595}=2\sqrt{595}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{595}}{2*-30}=\frac{50-2\sqrt{595}}{-60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{595}}{2*-30}=\frac{50+2\sqrt{595}}{-60}
$