2/5x-8=2x-10

Solution for 2/5x-8=2x-10 equation:

2/5x-8=2x-10

We move all terms to the left:

2/5x-8-(2x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-2x+10-8=0

We multiply all the terms by the denominator


-2x*5x+10*5x-8*5x+2=0

Wy multiply elements

-10x^2+50x-40x+2=0

We add all the numbers together, and all the variables

-10x^2+10x+2=0

a = -10; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·(-10)·2
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*-10}=\frac{-10-6\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*-10}=\frac{-10+6\sqrt{5}}{-20}
$