2x-16/5x+10=0

Solution for 2x-16/5x+10=0 equation:

2x-16/5x+10=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


2x*5x+10*5x-16=0

Wy multiply elements

10x^2+50x-16=0

a = 10; b = 50; c = -16;
Δ = b2-4ac
Δ = 502-4·10·(-16)
Δ = 3140
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:

$\sqrt{\Delta}=\sqrt{3140}=\sqrt{4*785}=\sqrt{4}*\sqrt{785}=2\sqrt{785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{785}}{2*10}=\frac{-50-2\sqrt{785}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{785}}{2*10}=\frac{-50+2\sqrt{785}}{20}
$