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-5/6x-1.9x=-102
We move all terms to the left:
-5/6x-1.9x-(-102)=0
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
-1.9x-5/6x+102=0
We multiply all the terms by the denominator
-(1.9x)*6x+102*6x-5=0
We add all the numbers together, and all the variables
-(+1.9x)*6x+102*6x-5=0
We multiply parentheses
-6x^2+102*6x-5=0
Wy multiply elements
-6x^2+612x-5=0
a = -6; b = 612; c = -5;
Δ = b2-4ac
Δ = 6122-4·(-6)·(-5)
Δ = 374424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{374424}=\sqrt{4*93606}=\sqrt{4}*\sqrt{93606}=2\sqrt{93606}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-2\sqrt{93606}}{2*-6}=\frac{-612-2\sqrt{93606}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+2\sqrt{93606}}{2*-6}=\frac{-612+2\sqrt{93606}}{-12} $
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