X2+5x-33=4x+9

Solution for X2+5x-33=4x+9 equation:

X2+5X-33=4X+9

We move all terms to the left:

X2+5X-33-(4X+9)=0

We add all the numbers together, and all the variables

X^2+5X-(4X+9)-33=0

We get rid of parentheses

X^2+5X-4X-9-33=0

We add all the numbers together, and all the variables

X^2+X-42=0

a = 1; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·1·(-42)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*1}=\frac{12}{2}
=6
$