-5x(-x+1)+4x+1=23

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Solution for -5x(-x+1)+4x+1=23 equation:



-5x(-x+1)+4x+1=23
We move all terms to the left:
-5x(-x+1)+4x+1-(23)=0
We add all the numbers together, and all the variables
-5x(-1x+1)+4x+1-23=0
We add all the numbers together, and all the variables
4x-5x(-1x+1)-22=0
We multiply parentheses
5x^2+4x-5x-22=0
We add all the numbers together, and all the variables
5x^2-1x-22=0
a = 5; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·5·(-22)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-21}{2*5}=\frac{-20}{10} =-2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+21}{2*5}=\frac{22}{10} =2+1/5 $

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