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x-15+1/2x=180
We move all terms to the left:
x-15+1/2x-(180)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
x+1/2x-195=0
We multiply all the terms by the denominator
x*2x-195*2x+1=0
Wy multiply elements
2x^2-390x+1=0
a = 2; b = -390; c = +1;
Δ = b2-4ac
Δ = -3902-4·2·1
Δ = 152092
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{152092}=\sqrt{4*38023}=\sqrt{4}*\sqrt{38023}=2\sqrt{38023}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-390)-2\sqrt{38023}}{2*2}=\frac{390-2\sqrt{38023}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-390)+2\sqrt{38023}}{2*2}=\frac{390+2\sqrt{38023}}{4} $
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