108x+6x^2=15x^2

Solution for 108x+6x^2=15x^2 equation:

108x+6x^2=15x^2

We move all terms to the left:

108x+6x^2-(15x^2)=0

determiningTheFunctionDomain
6x^2-15x^2+108x=0

We add all the numbers together, and all the variables

-9x^2+108x=0

a = -9; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-9)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-9}=\frac{-216}{-18}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-9}=\frac{0}{-18}
=0
$