10x-25/2x-5=0

Solution for 10x-25/2x-5=0 equation:

10x-25/2x-5=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x-5*2x-25=0

Wy multiply elements

20x^2-10x-25=0

a = 20; b = -10; c = -25;
Δ = b2-4ac
Δ = -102-4·20·(-25)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{21}}{2*20}=\frac{10-10\sqrt{21}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{21}}{2*20}=\frac{10+10\sqrt{21}}{40}
$