Q(x)=4/5x-9

Solution for Q(x)=4/5x-9 equation:

(Q)=4/5Q-9

We move all terms to the left:

(Q)-(4/5Q-9)=0


Domain of the equation: 5Q-9)!=0

Q∈R


We get rid of parentheses

Q-4/5Q+9=0

We multiply all the terms by the denominator


Q*5Q+9*5Q-4=0

Wy multiply elements

5Q^2+45Q-4=0

a = 5; b = 45; c = -4;
Δ = b2-4ac
Δ = 452-4·5·(-4)
Δ = 2105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2105}}{2*5}=\frac{-45-\sqrt{2105}}{10}
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2105}}{2*5}=\frac{-45+\sqrt{2105}}{10}
$