(5x-1)(x+2)=2

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Solution for (5x-1)(x+2)=2 equation:



(5x-1)(x+2)=2
We move all terms to the left:
(5x-1)(x+2)-(2)=0
We multiply parentheses ..
(+5x^2+10x-1x-2)-2=0
We get rid of parentheses
5x^2+10x-1x-2-2=0
We add all the numbers together, and all the variables
5x^2+9x-4=0
a = 5; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·5·(-4)
Δ = 161
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{-(9)-\sqrt{161}}{2*5}=\frac{-9-\sqrt{161}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{161}}{2*5}=\frac{-9+\sqrt{161}}{10} $

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