0.2x^2-x+3=-1.2x^2+5.5x-2

Solution for 0.2x^2-x+3=-1.2x^2+5.5x-2 equation:

0.2x^2-x+3=-1.2x^2+5.5x-2

We move all terms to the left:

0.2x^2-x+3-(-1.2x^2+5.5x-2)=0

We add all the numbers together, and all the variables

0.2x^2-(-1.2x^2+5.5x-2)-1x+3=0

We get rid of parentheses

0.2x^2+1.2x^2-5.5x-1x+2+3=0

We add all the numbers together, and all the variables

1.4x^2-6.5x+5=0

a = 1.4; b = -6.5; c = +5;
Δ = b2-4ac
Δ = -6.52-4·1.4·5
Δ = 14.25
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{-(-6.5)-\sqrt{14.25}}{2*1.4}=\frac{6.5-\sqrt{14.25}}{2.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.5)+\sqrt{14.25}}{2*1.4}=\frac{6.5+\sqrt{14.25}}{2.8}
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