X.3(2x+2)=9(2x-1)

Solution for X.3(2x+2)=9(2x-1) equation:

X.3(2X+2)=9(2X-1)

We move all terms to the left:

X.3(2X+2)-(9(2X-1))=0

We multiply parentheses

2X^2+2X-(9(2X-1))=0


We calculate terms in parentheses: -(9(2X-1)), so:

9(2X-1)

We multiply parentheses

18X-9

Back to the equation:

-(18X-9)


We get rid of parentheses

2X^2+2X-18X+9=0

We add all the numbers together, and all the variables

2X^2-16X+9=0

a = 2; b = -16; c = +9;
Δ = b2-4ac
Δ = -162-4·2·9
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{46}}{2*2}=\frac{16-2\sqrt{46}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{46}}{2*2}=\frac{16+2\sqrt{46}}{4}
$