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1/2x+10=3x
We move all terms to the left:
1/2x+10-(3x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-3x+1/2x+10=0
We multiply all the terms by the denominator
-3x*2x+10*2x+1=0
Wy multiply elements
-6x^2+20x+1=0
a = -6; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·(-6)·1
Δ = 424
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{106}}{2*-6}=\frac{-20-2\sqrt{106}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{106}}{2*-6}=\frac{-20+2\sqrt{106}}{-12} $
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