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7/2x=x+5

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Solution for 7/2x=x+5 equation:



7/2x=x+5
We move all terms to the left:
7/2x-(x+5)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
7/2x-x-5=0
We multiply all the terms by the denominator
-x*2x-5*2x+7=0
Wy multiply elements
-2x^2-10x+7=0
a = -2; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-2)·7
Δ = 156
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{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*-2}=\frac{10-2\sqrt{39}}{-4}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*-2}=\frac{10+2\sqrt{39}}{-4}

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