5x-15/2x-5=0

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Solution for 5x-15/2x-5=0 equation:



5x-15/2x-5=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We multiply all the terms by the denominator
5x*2x-5*2x-15=0
Wy multiply elements
10x^2-10x-15=0
a = 10; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·10·(-15)
Δ = 700
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:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*10}=\frac{10-10\sqrt{7}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*10}=\frac{10+10\sqrt{7}}{20} $

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