x^2=2(3x-4)

Solution for x^2=2(3x-4) equation:

x^2=2(3x-4)

We move all terms to the left:

x^2-(2(3x-4))=0


We calculate terms in parentheses: -(2(3x-4)), so:

2(3x-4)

We multiply parentheses

6x-8

Back to the equation:

-(6x-8)


We get rid of parentheses

x^2-6x+8=0

a = 1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·1·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*1}=\frac{8}{2}
=4
$