x(x+18)=3/5

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

x(x+18)=3/5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+90x-3=0

a = 5; b = 90; c = -3;
Δ = b2-4ac
Δ = 902-4·5·(-3)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-4\sqrt{510}}{2*5}=\frac{-90-4\sqrt{510}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+4\sqrt{510}}{2*5}=\frac{-90+4\sqrt{510}}{10}
$