8/5x-10x=-38

Solution for 8/5x-10x=-38 equation:

8/5x-10x=-38

We move all terms to the left:

8/5x-10x-(-38)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+8/5x+38=0

We multiply all the terms by the denominator


-10x*5x+38*5x+8=0

Wy multiply elements

-50x^2+190x+8=0

a = -50; b = 190; c = +8;
Δ = b2-4ac
Δ = 1902-4·(-50)·8
Δ = 37700
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:

$\sqrt{\Delta}=\sqrt{37700}=\sqrt{100*377}=\sqrt{100}*\sqrt{377}=10\sqrt{377}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-10\sqrt{377}}{2*-50}=\frac{-190-10\sqrt{377}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+10\sqrt{377}}{2*-50}=\frac{-190+10\sqrt{377}}{-100}
$