-2.4x^2-7.7x+3.1=-4.1

Solution for -2.4x^2-7.7x+3.1=-4.1 equation:

-2.4x^2-7.7x+3.1=-4.1

We move all terms to the left:

-2.4x^2-7.7x+3.1-(-4.1)=0

We add all the numbers together, and all the variables

-2.4x^2-7.7x+7.2=0

a = -2.4; b = -7.7; c = +7.2;
Δ = b2-4ac
Δ = -7.72-4·(-2.4)·7.2
Δ = 128.41
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{-(-7.7)-\sqrt{128.41}}{2*-2.4}=\frac{7.7-\sqrt{128.41}}{-4.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.7)+\sqrt{128.41}}{2*-2.4}=\frac{7.7+\sqrt{128.41}}{-4.8}
$