12x+x^2=15x^2

Solution for 12x+x^2=15x^2 equation:

12x+x^2=15x^2

We move all terms to the left:

12x+x^2-(15x^2)=0

determiningTheFunctionDomain
x^2-15x^2+12x=0

We add all the numbers together, and all the variables

-14x^2+12x=0

a = -14; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-14)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-14}=\frac{-24}{-28}
=6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-14}=\frac{0}{-28}
=0
$