x+9/2x-10=0

Solution for x+9/2x-10=0 equation:

x+9/2x-10=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-10*2x+9=0

Wy multiply elements

2x^2-20x+9=0

a = 2; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·2·9
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{82}}{2*2}=\frac{20-2\sqrt{82}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{82}}{2*2}=\frac{20+2\sqrt{82}}{4}
$