5x(x-2)=3x+18

Solution for 5x(x-2)=3x+18 equation:

5x(x-2)=3x+18

We move all terms to the left:

5x(x-2)-(3x+18)=0

We multiply parentheses

5x^2-10x-(3x+18)=0

We get rid of parentheses

5x^2-10x-3x-18=0

We add all the numbers together, and all the variables

5x^2-13x-18=0

a = 5; b = -13; c = -18;
Δ = b2-4ac
Δ = -132-4·5·(-18)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*5}=\frac{36}{10}
=3+3/5
$