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3/3.5x=4x+8
We move all terms to the left:
3/3.5x-(4x+8)=0
Domain of the equation: 3.5x!=0We get rid of parentheses
x!=0/3.5
x!=0
x∈R
3/3.5x-4x-8=0
We multiply all the terms by the denominator
-4x*3.5x-8*3.5x+3=0
Wy multiply elements
-12x^2-24x+3=0
a = -12; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-12)·3
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*-12}=\frac{24-12\sqrt{5}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*-12}=\frac{24+12\sqrt{5}}{-24} $
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