0=5x^2+2x-3

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



0=5x^2+2x-3
We move all terms to the left:
0-(5x^2+2x-3)=0
We add all the numbers together, and all the variables
-(5x^2+2x-3)=0
We get rid of parentheses
-5x^2-2x+3=0
a = -5; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-5)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*-5}=\frac{-6}{-10} =3/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*-5}=\frac{10}{-10} =-1 $

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