0.5x2-4x-1=-0.2x2+2x+3

Solution for 0.5x2-4x-1=-0.2x2+2x+3 equation:

0.5x^2-4x-1=-0.2x^2+2x+3

We move all terms to the left:

0.5x^2-4x-1-(-0.2x^2+2x+3)=0

We get rid of parentheses

0.5x^2+0.2x^2-2x-4x-3-1=0

We add all the numbers together, and all the variables

0.7x^2-6x-4=0

a = 0.7; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·0.7·(-4)
Δ = 47.2
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{-(-6)-\sqrt{47.2}}{2*0.7}=\frac{6-\sqrt{47.2}}{1.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{47.2}}{2*0.7}=\frac{6+\sqrt{47.2}}{1.4}
$