4x+5x2-3=3x-2x2

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Solution for 4x+5x2-3=3x-2x2 equation:



4x+5x^2-3=3x-2x^2
We move all terms to the left:
4x+5x^2-3-(3x-2x^2)=0
We get rid of parentheses
5x^2+2x^2-3x+4x-3=0
We add all the numbers together, and all the variables
7x^2+x-3=0
a = 7; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·7·(-3)
Δ = 85
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{-(1)-\sqrt{85}}{2*7}=\frac{-1-\sqrt{85}}{14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{85}}{2*7}=\frac{-1+\sqrt{85}}{14} $

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