4x(x+5)=2x+17+2x-3x

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Solution for 4x(x+5)=2x+17+2x-3x equation:



4x(x+5)=2x+17+2x-3x
We move all terms to the left:
4x(x+5)-(2x+17+2x-3x)=0
We add all the numbers together, and all the variables
4x(x+5)-(x+17)=0
We multiply parentheses
4x^2+20x-(x+17)=0
We get rid of parentheses
4x^2+20x-x-17=0
We add all the numbers together, and all the variables
4x^2+19x-17=0
a = 4; b = 19; c = -17;
Δ = b2-4ac
Δ = 192-4·4·(-17)
Δ = 633
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{-(19)-\sqrt{633}}{2*4}=\frac{-19-\sqrt{633}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{633}}{2*4}=\frac{-19+\sqrt{633}}{8} $

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