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2x+8=6x-12-13/2x
We move all terms to the left:
2x+8-(6x-12-13/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2x-(6x-13/2x-12)+8=0
We get rid of parentheses
2x-6x+13/2x+12+8=0
We multiply all the terms by the denominator
2x*2x-6x*2x+12*2x+8*2x+13=0
Wy multiply elements
4x^2-12x^2+24x+16x+13=0
We add all the numbers together, and all the variables
-8x^2+40x+13=0
a = -8; b = 40; c = +13;
Δ = b2-4ac
Δ = 402-4·(-8)·13
Δ = 2016
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12\sqrt{14}}{2*-8}=\frac{-40-12\sqrt{14}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12\sqrt{14}}{2*-8}=\frac{-40+12\sqrt{14}}{-16} $
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