5q-1=2-q(q-1)

Solution for 5q-1=2-q(q-1) equation:

5q-1=2-q(q-1)

We move all terms to the left:

5q-1-(2-q(q-1))=0


We calculate terms in parentheses: -(2-q(q-1)), so:

2-q(q-1)

determiningTheFunctionDomain
-q(q-1)+2

We multiply parentheses

-q^2+1q+2

We add all the numbers together, and all the variables

-1q^2+q+2

Back to the equation:

-(-1q^2+q+2)


We get rid of parentheses

1q^2-q+5q-2-1=0

We add all the numbers together, and all the variables

q^2+4q-3=0

a = 1; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·1·(-3)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*1}=\frac{-4-2\sqrt{7}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*1}=\frac{-4+2\sqrt{7}}{2}
$