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x+7-1/2x=22
We move all terms to the left:
x+7-1/2x-(22)=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-15=0
We multiply all the terms by the denominator
x*2x-15*2x-1=0
Wy multiply elements
2x^2-30x-1=0
a = 2; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·2·(-1)
Δ = 908
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{227}}{2*2}=\frac{30-2\sqrt{227}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{227}}{2*2}=\frac{30+2\sqrt{227}}{4} $
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