2x(x-1)+5x=3x+6

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Solution for 2x(x-1)+5x=3x+6 equation:



2x(x-1)+5x=3x+6
We move all terms to the left:
2x(x-1)+5x-(3x+6)=0
We add all the numbers together, and all the variables
5x+2x(x-1)-(3x+6)=0
We multiply parentheses
2x^2+5x-2x-(3x+6)=0
We get rid of parentheses
2x^2+5x-2x-3x-6=0
We add all the numbers together, and all the variables
2x^2-6=0
a = 2; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·2·(-6)
Δ = 48
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:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*2}=\frac{0-4\sqrt{3}}{4} =-\frac{4\sqrt{3}}{4} =-\sqrt{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*2}=\frac{0+4\sqrt{3}}{4} =\frac{4\sqrt{3}}{4} =\sqrt{3} $

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