X^2+72x+144=16/9

Solution for X^2+72x+144=16/9 equation:

X^2+72X+144=16/9

We move all terms to the left:

X^2+72X+144-(16/9)=0

We add all the numbers together, and all the variables

X^2+72X+144-(+16/9)=0

We get rid of parentheses

X^2+72X+144-16/9=0

We multiply all the terms by the denominator


X^2*9+72X*9-16+144*9=0

We add all the numbers together, and all the variables

X^2*9+72X*9+1280=0

Wy multiply elements

9X^2+648X+1280=0

a = 9; b = 648; c = +1280;
Δ = b2-4ac
Δ = 6482-4·9·1280
Δ = 373824
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:

$\sqrt{\Delta}=\sqrt{373824}=\sqrt{576*649}=\sqrt{576}*\sqrt{649}=24\sqrt{649}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(648)-24\sqrt{649}}{2*9}=\frac{-648-24\sqrt{649}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(648)+24\sqrt{649}}{2*9}=\frac{-648+24\sqrt{649}}{18}
$