(6x+13)/2x+3=2x+3

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Solution for (6x+13)/2x+3=2x+3 equation:



(6x+13)/2x+3=2x+3
We move all terms to the left:
(6x+13)/2x+3-(2x+3)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
(6x+13)/2x-2x-3+3=0
We multiply all the terms by the denominator
(6x+13)-2x*2x-3*2x+3*2x=0
Wy multiply elements
-4x^2+(6x+13)-6x+6x=0
We get rid of parentheses
-4x^2+6x-6x+6x+13=0
We add all the numbers together, and all the variables
-4x^2+6x+13=0
a = -4; b = 6; c = +13;
Δ = b2-4ac
Δ = 62-4·(-4)·13
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{-(6)-2\sqrt{61}}{2*-4}=\frac{-6-2\sqrt{61}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{61}}{2*-4}=\frac{-6+2\sqrt{61}}{-8} $

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