2x-5x2+3+4x=0

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Solution for 2x-5x2+3+4x=0 equation:



2x-5x^2+3+4x=0
We add all the numbers together, and all the variables
-5x^2+6x+3=0
a = -5; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-5)·3
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*-5}=\frac{-6-4\sqrt{6}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*-5}=\frac{-6+4\sqrt{6}}{-10} $

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