X^2=2(3x-2)

Solution for X^2=2(3x-2) equation:

X^2=2(3X-2)

We move all terms to the left:

X^2-(2(3X-2))=0


We calculate terms in parentheses: -(2(3X-2)), so:

2(3X-2)

We multiply parentheses

6X-4

Back to the equation:

-(6X-4)


We get rid of parentheses

X^2-6X+4=0

a = 1; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·1·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*1}=\frac{6-2\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*1}=\frac{6+2\sqrt{5}}{2}
$