X+3/5x=26

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

X+3/5X=26

We move all terms to the left:

X+3/5X-(26)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We multiply all the terms by the denominator


X*5X-26*5X+3=0

Wy multiply elements

5X^2-130X+3=0

a = 5; b = -130; c = +3;
Δ = b2-4ac
Δ = -1302-4·5·3
Δ = 16840
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:

$\sqrt{\Delta}=\sqrt{16840}=\sqrt{4*4210}=\sqrt{4}*\sqrt{4210}=2\sqrt{4210}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4210}}{2*5}=\frac{130-2\sqrt{4210}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4210}}{2*5}=\frac{130+2\sqrt{4210}}{10}
$