5(a+3)=a(a-2)

Solution for 5(a+3)=a(a-2) equation:

5(a+3)=a(a-2)

We move all terms to the left:

5(a+3)-(a(a-2))=0

We multiply parentheses

5a-(a(a-2))+15=0


We calculate terms in parentheses: -(a(a-2)), so:

a(a-2)

We multiply parentheses

a^2-2a

Back to the equation:

-(a^2-2a)


We get rid of parentheses

-a^2+5a+2a+15=0

We add all the numbers together, and all the variables

-1a^2+7a+15=0

a = -1; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-1)·15
Δ = 109
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{-(7)-\sqrt{109}}{2*-1}=\frac{-7-\sqrt{109}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*-1}=\frac{-7+\sqrt{109}}{-2}
$