(x+18)x=5/2

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

(x+18)x=5/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+36x-5=0

a = 2; b = 36; c = -5;
Δ = b2-4ac
Δ = 362-4·2·(-5)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{334}}{2*2}=\frac{-36-2\sqrt{334}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{334}}{2*2}=\frac{-36+2\sqrt{334}}{4}
$