12+0.3x+0.27x^2=15x-0.2x^2

Solution for 12+0.3x+0.27x^2=15x-0.2x^2 equation:

12+0.3x+0.27x^2=15x-0.2x^2

We move all terms to the left:

12+0.3x+0.27x^2-(15x-0.2x^2)=0

We get rid of parentheses

0.27x^2+0.2x^2-15x+0.3x+12=0

We add all the numbers together, and all the variables

0.47x^2-14.7x+12=0

a = 0.47; b = -14.7; c = +12;
Δ = b2-4ac
Δ = -14.72-4·0.47·12
Δ = 193.53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14.7)-\sqrt{193.53}}{2*0.47}=\frac{14.7-\sqrt{193.53}}{0.94}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.7)+\sqrt{193.53}}{2*0.47}=\frac{14.7+\sqrt{193.53}}{0.94}
$