9x^2=2(9x-4)

Solution for 9x^2=2(9x-4) equation:

9x^2=2(9x-4)

We move all terms to the left:

9x^2-(2(9x-4))=0


We calculate terms in parentheses: -(2(9x-4)), so:

2(9x-4)

We multiply parentheses

18x-8

Back to the equation:

-(18x-8)


We get rid of parentheses

9x^2-18x+8=0

a = 9; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·9·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*9}=\frac{12}{18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*9}=\frac{24}{18}
=1+1/3
$