q(2q-3)=2(4q-1)

Solution for q(2q-3)=2(4q-1) equation:

q(2q-3)=2(4q-1)

We move all terms to the left:

q(2q-3)-(2(4q-1))=0

We multiply parentheses

2q^2-3q-(2(4q-1))=0


We calculate terms in parentheses: -(2(4q-1)), so:

2(4q-1)

We multiply parentheses

8q-2

Back to the equation:

-(8q-2)


We get rid of parentheses

2q^2-3q-8q+2=0

We add all the numbers together, and all the variables

2q^2-11q+2=0

a = 2; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·2·2
Δ = 105
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{-(-11)-\sqrt{105}}{2*2}=\frac{11-\sqrt{105}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{105}}{2*2}=\frac{11+\sqrt{105}}{4}
$