5(a-1)-a(a-2)=-3(2a+1)-2

Solution for 5(a-1)-a(a-2)=-3(2a+1)-2 equation:

5(a-1)-a(a-2)=-3(2a+1)-2

We move all terms to the left:

5(a-1)-a(a-2)-(-3(2a+1)-2)=0

We multiply parentheses

-a^2+5a+2a-(-3(2a+1)-2)-5=0


We calculate terms in parentheses: -(-3(2a+1)-2), so:

-3(2a+1)-2

We multiply parentheses

-6a-3-2

We add all the numbers together, and all the variables

-6a-5

Back to the equation:

-(-6a-5)


We add all the numbers together, and all the variables

-1a^2+7a-(-6a-5)-5=0

We get rid of parentheses

-1a^2+7a+6a+5-5=0

We add all the numbers together, and all the variables

-1a^2+13a=0

a = -1; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1}=\frac{-26}{-2}
=+13
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1}=\frac{0}{-2}
=0
$