-2/5x+3=23x+13.

Solution for -2/5x+3=23x+13. equation:

-2/5x+3=23x+13.

We move all terms to the left:

-2/5x+3-(23x+13.)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2/5x-(23x+13)+3=0

We get rid of parentheses

-2/5x-23x-13+3=0

We multiply all the terms by the denominator


-23x*5x-13*5x+3*5x-2=0

Wy multiply elements

-115x^2-65x+15x-2=0

We add all the numbers together, and all the variables

-115x^2-50x-2=0

a = -115; b = -50; c = -2;
Δ = b2-4ac
Δ = -502-4·(-115)·(-2)
Δ = 1580
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:

$\sqrt{\Delta}=\sqrt{1580}=\sqrt{4*395}=\sqrt{4}*\sqrt{395}=2\sqrt{395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{395}}{2*-115}=\frac{50-2\sqrt{395}}{-230}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{395}}{2*-115}=\frac{50+2\sqrt{395}}{-230}
$