X2+3x=29-x2

Solution for X2+3x=29-x2 equation:

X2+3X=29-X2

We move all terms to the left:

X2+3X-(29-X2)=0

We add all the numbers together, and all the variables

-(-1X^2+29)+X2+3X=0

We add all the numbers together, and all the variables

X^2-(-1X^2+29)+3X=0

We get rid of parentheses

X^2+1X^2+3X-29=0

We add all the numbers together, and all the variables

2X^2+3X-29=0

a = 2; b = 3; c = -29;
Δ = b2-4ac
Δ = 32-4·2·(-29)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{241}}{2*2}=\frac{-3-\sqrt{241}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{241}}{2*2}=\frac{-3+\sqrt{241}}{4}
$