3/5x+26=2x

Solution for 3/5x+26=2x equation:

3/5x+26=2x

We move all terms to the left:

3/5x+26-(2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/5x+26=0

We multiply all the terms by the denominator


-2x*5x+26*5x+3=0

Wy multiply elements

-10x^2+130x+3=0

a = -10; b = 130; c = +3;
Δ = b2-4ac
Δ = 1302-4·(-10)·3
Δ = 17020
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:

$\sqrt{\Delta}=\sqrt{17020}=\sqrt{4*4255}=\sqrt{4}*\sqrt{4255}=2\sqrt{4255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{4255}}{2*-10}=\frac{-130-2\sqrt{4255}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{4255}}{2*-10}=\frac{-130+2\sqrt{4255}}{-20}
$