12x-1,8x^2=-9,1

Solution for 12x-1,8x^2=-9,1 equation:

12x-1.8x^2=-9.1

We move all terms to the left:

12x-1.8x^2-(-9.1)=0

We add all the numbers together, and all the variables

-1.8x^2+12x+9.1=0

a = -1.8; b = 12; c = +9.1;
Δ = b2-4ac
Δ = 122-4·(-1.8)·9.1
Δ = 209.52
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{-(12)-\sqrt{209.52}}{2*-1.8}=\frac{-12-\sqrt{209.52}}{-3.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+\sqrt{209.52}}{2*-1.8}=\frac{-12+\sqrt{209.52}}{-3.6}
$