X^2+3x-19=29

Solution for X^2+3x-19=29 equation:

X^2+3X-19=29

We move all terms to the left:

X^2+3X-19-(29)=0

We add all the numbers together, and all the variables

X^2+3X-48=0

a = 1; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·1·(-48)
Δ = 201
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{201}}{2*1}=\frac{-3-\sqrt{201}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*1}=\frac{-3+\sqrt{201}}{2}
$