18=3+5x(x-18)

Solution for 18=3+5x(x-18) equation:

18=3+5x(x-18)

We move all terms to the left:

18-(3+5x(x-18))=0


We calculate terms in parentheses: -(3+5x(x-18)), so:

3+5x(x-18)

determiningTheFunctionDomain
5x(x-18)+3

We multiply parentheses

5x^2-90x+3

Back to the equation:

-(5x^2-90x+3)


We get rid of parentheses

-5x^2+90x-3+18=0

We add all the numbers together, and all the variables

-5x^2+90x+15=0

a = -5; b = 90; c = +15;
Δ = b2-4ac
Δ = 902-4·(-5)·15
Δ = 8400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-20\sqrt{21}}{2*-5}=\frac{-90-20\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+20\sqrt{21}}{2*-5}=\frac{-90+20\sqrt{21}}{-10}
$