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

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



2x(x+5)=6x+4
We move all terms to the left:
2x(x+5)-(6x+4)=0
We multiply parentheses
2x^2+10x-(6x+4)=0
We get rid of parentheses
2x^2+10x-6x-4=0
We add all the numbers together, and all the variables
2x^2+4x-4=0
a = 2; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·2·(-4)
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{-(4)-4\sqrt{3}}{2*2}=\frac{-4-4\sqrt{3}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*2}=\frac{-4+4\sqrt{3}}{4} $

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