3/5x-10=-4x-+-8

Solution for 3/5x-10=-4x-+-8 equation:

3/5x-10=-4x-+-8

We move all terms to the left:

3/5x-10-(-4x-+-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-4x)-10=0

We get rid of parentheses

3/5x+4x-10=0

We multiply all the terms by the denominator


4x*5x-10*5x+3=0

Wy multiply elements

20x^2-50x+3=0

a = 20; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·20·3
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{565}}{2*20}=\frac{50-2\sqrt{565}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{565}}{2*20}=\frac{50+2\sqrt{565}}{40}
$