a+5=(1/5)(15+5a)

Solution for a+5=(1/5)(15+5a) equation:

a+5=(1/5)(15+5a)

We move all terms to the left:

a+5-((1/5)(15+5a))=0


Domain of the equation: 5)(15+5a))!=0

a∈R


We add all the numbers together, and all the variables

a-((+1/5)(5a+15))+5=0

We multiply parentheses ..

-((+5a^2+1/5*15))+a+5=0

We multiply all the terms by the denominator


-((+5a^2+1+a*5*15))+5*5*15))=0


We calculate terms in parentheses: -((+5a^2+1+a*5*15)), so:

(+5a^2+1+a*5*15)

We get rid of parentheses

5a^2+a*5*15+1

Wy multiply elements

5a^2+75a*1+1

Wy multiply elements

5a^2+75a+1

Back to the equation:

-(5a^2+75a+1)


We add all the numbers together, and all the variables

-(5a^2+75a+1)=0

We get rid of parentheses

-5a^2-75a-1=0

a = -5; b = -75; c = -1;
Δ = b2-4ac
Δ = -752-4·(-5)·(-1)
Δ = 5605
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5605}}{2*-5}=\frac{75-\sqrt{5605}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5605}}{2*-5}=\frac{75+\sqrt{5605}}{-10}
$