(38+x)x=3(x2)

Solution for (38+x)x=3(x2) equation:

(38+x)x=3(x2)

We move all terms to the left:

(38+x)x-(3(x2))=0

determiningTheFunctionDomain
(38+x)x-3x2=0

We add all the numbers together, and all the variables

(x+38)x-3x2=0

We add all the numbers together, and all the variables

-3x^2+(x+38)x=0

We multiply parentheses

-3x^2+x^2+38x=0

We add all the numbers together, and all the variables

-2x^2+38x=0

a = -2; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-2)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-2}=\frac{-76}{-4}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-2}=\frac{0}{-4}
=0
$