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3/2x+30+x=90
We move all terms to the left:
3/2x+30+x-(90)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
x+3/2x-60=0
We multiply all the terms by the denominator
x*2x-60*2x+3=0
Wy multiply elements
2x^2-120x+3=0
a = 2; b = -120; c = +3;
Δ = b2-4ac
Δ = -1202-4·2·3
Δ = 14376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14376}=\sqrt{4*3594}=\sqrt{4}*\sqrt{3594}=2\sqrt{3594}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3594}}{2*2}=\frac{120-2\sqrt{3594}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3594}}{2*2}=\frac{120+2\sqrt{3594}}{4} $
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