x^2-3x=14/9

Solution for x^2-3x=14/9 equation:

x^2-3x=14/9

We move all terms to the left:

x^2-3x-(14/9)=0

We add all the numbers together, and all the variables

x^2-3x-(+14/9)=0

We get rid of parentheses

x^2-3x-14/9=0

We multiply all the terms by the denominator


x^2*9-3x*9-14=0

Wy multiply elements

9x^2-27x-14=0

a = 9; b = -27; c = -14;
Δ = b2-4ac
Δ = -272-4·9·(-14)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{137}}{2*9}=\frac{27-3\sqrt{137}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{137}}{2*9}=\frac{27+3\sqrt{137}}{18}
$