45-0.18x^2=0.12x^2+1.5x

Solution for 45-0.18x^2=0.12x^2+1.5x equation:

45-0.18x^2=0.12x^2+1.5x

We move all terms to the left:

45-0.18x^2-(0.12x^2+1.5x)=0

We get rid of parentheses

-0.18x^2-0.12x^2-1.5x+45=0

We add all the numbers together, and all the variables

-0.3x^2-1.5x+45=0

a = -0.3; b = -1.5; c = +45;
Δ = b2-4ac
Δ = -1.52-4·(-0.3)·45
Δ = 56.25
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{-(-1.5)-\sqrt{56.25}}{2*-0.3}=\frac{1.5-\sqrt{56.25}}{-0.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{56.25}}{2*-0.3}=\frac{1.5+\sqrt{56.25}}{-0.6}
$