5x(x+2)+4x=6x+1

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Solution for 5x(x+2)+4x=6x+1 equation:



5x(x+2)+4x=6x+1
We move all terms to the left:
5x(x+2)+4x-(6x+1)=0
We add all the numbers together, and all the variables
4x+5x(x+2)-(6x+1)=0
We multiply parentheses
5x^2+4x+10x-(6x+1)=0
We get rid of parentheses
5x^2+4x+10x-6x-1=0
We add all the numbers together, and all the variables
5x^2+8x-1=0
a = 5; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·5·(-1)
Δ = 84
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:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{21}}{2*5}=\frac{-8-2\sqrt{21}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{21}}{2*5}=\frac{-8+2\sqrt{21}}{10} $

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