x^2-2.4x=3.58x^2+40.096x+107.1136

Solution for x^2-2.4x=3.58x^2+40.096x+107.1136 equation:

x^2-2.4x=3.58x^2+40.096x+107.1136

We move all terms to the left:

x^2-2.4x-(3.58x^2+40.096x+107.1136)=0

We get rid of parentheses

x^2-3.58x^2-2.4x-40.096x-107.1136=0

We add all the numbers together, and all the variables

-2.58x^2-42.496x-107.1136=0

a = -2.58; b = -42.496; c = -107.1136;
Δ = b2-4ac
Δ = -42.4962-4·(-2.58)·(-107.1136)
Δ = 700.497664
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{-(-42.496)-\sqrt{700.497664}}{2*-2.58}=\frac{42.496-\sqrt{700.497664}}{-5.16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42.496)+\sqrt{700.497664}}{2*-2.58}=\frac{42.496+\sqrt{700.497664}}{-5.16}
$