10x+15/20x-8=0

Solution for 10x+15/20x-8=0 equation:

10x+15/20x-8=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We multiply all the terms by the denominator


10x*20x-8*20x+15=0

Wy multiply elements

200x^2-160x+15=0

a = 200; b = -160; c = +15;
Δ = b2-4ac
Δ = -1602-4·200·15
Δ = 13600
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:

$\sqrt{\Delta}=\sqrt{13600}=\sqrt{400*34}=\sqrt{400}*\sqrt{34}=20\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-20\sqrt{34}}{2*200}=\frac{160-20\sqrt{34}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+20\sqrt{34}}{2*200}=\frac{160+20\sqrt{34}}{400}
$