X^2+2x=352/9

Solution for X^2+2x=352/9 equation:

X^2+2X=352/9

We move all terms to the left:

X^2+2X-(352/9)=0

We add all the numbers together, and all the variables

X^2+2X-(+352/9)=0

We get rid of parentheses

X^2+2X-352/9=0

We multiply all the terms by the denominator


X^2*9+2X*9-352=0

Wy multiply elements

9X^2+18X-352=0

a = 9; b = 18; c = -352;
Δ = b2-4ac
Δ = 182-4·9·(-352)
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-114}{2*9}=\frac{-132}{18}
=-7+1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+114}{2*9}=\frac{96}{18}
=5+1/3
$