X^2-2x+(4x/9)=1

Solution for X^2-2x+(4x/9)=1 equation:

X^2-2X+(4X/9)=1

We move all terms to the left:

X^2-2X+(4X/9)-(1)=0

We add all the numbers together, and all the variables

X^2-2X+(+4X/9)-1=0

We get rid of parentheses

X^2-2X+4X/9-1=0

We multiply all the terms by the denominator


X^2*9-2X*9+4X-1*9=0

We add all the numbers together, and all the variables

X^2*9+4X-2X*9-9=0

Wy multiply elements

9X^2+4X-18X-9=0

We add all the numbers together, and all the variables

9X^2-14X-9=0

a = 9; b = -14; c = -9;
Δ = b2-4ac
Δ = -142-4·9·(-9)
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{130}}{2*9}=\frac{14-2\sqrt{130}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{130}}{2*9}=\frac{14+2\sqrt{130}}{18}
$