a(22+a)=4(5a+6)

Solution for a(22+a)=4(5a+6) equation:

a(22+a)=4(5a+6)

We move all terms to the left:

a(22+a)-(4(5a+6))=0

We add all the numbers together, and all the variables

a(a+22)-(4(5a+6))=0

We multiply parentheses

a^2+22a-(4(5a+6))=0


We calculate terms in parentheses: -(4(5a+6)), so:

4(5a+6)

We multiply parentheses

20a+24

Back to the equation:

-(20a+24)


We get rid of parentheses

a^2+22a-20a-24=0

We add all the numbers together, and all the variables

a^2+2a-24=0

a = 1; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*1}=\frac{-12}{2}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*1}=\frac{8}{2}
=4
$