(x+3x^2)=(15+x)

Solution for (x+3x^2)=(15+x) equation:

(x+3x^2)=(15+x)

We move all terms to the left:

(x+3x^2)-((15+x))=0

We add all the numbers together, and all the variables

(x+3x^2)-((x+15))=0

We get rid of parentheses

3x^2+x-((x+15))=0


We calculate terms in parentheses: -((x+15)), so:

(x+15)

We get rid of parentheses

x+15

Back to the equation:

-(x+15)


We get rid of parentheses

3x^2+x-x-15=0

We add all the numbers together, and all the variables

3x^2-15=0

a = 3; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·3·(-15)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*3}=\frac{0-6\sqrt{5}}{6}
=-\frac{6\sqrt{5}}{6}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*3}=\frac{0+6\sqrt{5}}{6}
=\frac{6\sqrt{5}}{6}
=\sqrt{5}
$