X2-9x+33=4x+3

Solution for X2-9x+33=4x+3 equation:

X2-9X+33=4X+3

We move all terms to the left:

X2-9X+33-(4X+3)=0

We add all the numbers together, and all the variables

X^2-9X-(4X+3)+33=0

We get rid of parentheses

X^2-9X-4X-3+33=0

We add all the numbers together, and all the variables

X^2-13X+30=0

a = 1; b = -13; c = +30;
Δ = b2-4ac
Δ = -132-4·1·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*1}=\frac{20}{2}
=10
$