2/5x-10=13x

Solution for 2/5x-10=13x equation:

2/5x-10=13x

We move all terms to the left:

2/5x-10-(13x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-13x+2/5x-10=0

We multiply all the terms by the denominator


-13x*5x-10*5x+2=0

Wy multiply elements

-65x^2-50x+2=0

a = -65; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-65)·2
Δ = 3020
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:

$\sqrt{\Delta}=\sqrt{3020}=\sqrt{4*755}=\sqrt{4}*\sqrt{755}=2\sqrt{755}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{755}}{2*-65}=\frac{50-2\sqrt{755}}{-130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{755}}{2*-65}=\frac{50+2\sqrt{755}}{-130}
$