Q(x)=1/2x-3

Solution for Q(x)=1/2x-3 equation:

(Q)=1/2Q-3

We move all terms to the left:

(Q)-(1/2Q-3)=0


Domain of the equation: 2Q-3)!=0

Q∈R


We get rid of parentheses

Q-1/2Q+3=0

We multiply all the terms by the denominator


Q*2Q+3*2Q-1=0

Wy multiply elements

2Q^2+6Q-1=0

a = 2; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$Q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*2}=\frac{-6-2\sqrt{11}}{4}
$
$Q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*2}=\frac{-6+2\sqrt{11}}{4}
$