6x+10=2x(3x+4)

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Solution for 6x+10=2x(3x+4) equation:



6x+10=2x(3x+4)
We move all terms to the left:
6x+10-(2x(3x+4))=0
We calculate terms in parentheses: -(2x(3x+4)), so:
2x(3x+4)
We multiply parentheses
6x^2+8x
Back to the equation:
-(6x^2+8x)
We get rid of parentheses
-6x^2+6x-8x+10=0
We add all the numbers together, and all the variables
-6x^2-2x+10=0
a = -6; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-6)·10
Δ = 244
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:
$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*-6}=\frac{2-2\sqrt{61}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*-6}=\frac{2+2\sqrt{61}}{-12} $

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