5x+33=3x(6x-10)+11

Solution for 5x+33=3x(6x-10)+11 equation:

5x+33=3x(6x-10)+11

We move all terms to the left:

5x+33-(3x(6x-10)+11)=0


We calculate terms in parentheses: -(3x(6x-10)+11), so:

3x(6x-10)+11

We multiply parentheses

18x^2-30x+11

Back to the equation:

-(18x^2-30x+11)


We get rid of parentheses

-18x^2+5x+30x-11+33=0

We add all the numbers together, and all the variables

-18x^2+35x+22=0

a = -18; b = 35; c = +22;
Δ = b2-4ac
Δ = 352-4·(-18)·22
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-53}{2*-18}=\frac{-88}{-36}
=2+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+53}{2*-18}=\frac{18}{-36}
=-1/2
$