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x=5/6x-8
We move all terms to the left:
x-(5/6x-8)=0
Domain of the equation: 6x-8)!=0We get rid of parentheses
x∈R
x-5/6x+8=0
We multiply all the terms by the denominator
x*6x+8*6x-5=0
Wy multiply elements
6x^2+48x-5=0
a = 6; b = 48; c = -5;
Δ = b2-4ac
Δ = 482-4·6·(-5)
Δ = 2424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{606}}{2*6}=\frac{-48-2\sqrt{606}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{606}}{2*6}=\frac{-48+2\sqrt{606}}{12} $
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