(2x(x+29))/(x-3)=0

Solution for (2x(x+29))/(x-3)=0 equation:

(2x(x+29))/(x-3)=0


Domain of the equation: (x-3)!=0

We move all terms containing x to the left, all other terms to the right

x!=3

x∈R


We multiply all the terms by the denominator


(2x(x+29))=0


We calculate terms in parentheses: +(2x(x+29)), so:

2x(x+29)

We multiply parentheses

2x^2+58x

Back to the equation:

+(2x^2+58x)


We get rid of parentheses

2x^2+58x=0

a = 2; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·2·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*2}=\frac{-116}{4}
=-29
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*2}=\frac{0}{4}
=0
$