2/5x+38=8x

Solution for 2/5x+38=8x equation:

2/5x+38=8x

We move all terms to the left:

2/5x+38-(8x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-8x+2/5x+38=0

We multiply all the terms by the denominator


-8x*5x+38*5x+2=0

Wy multiply elements

-40x^2+190x+2=0

a = -40; b = 190; c = +2;
Δ = b2-4ac
Δ = 1902-4·(-40)·2
Δ = 36420
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:

$\sqrt{\Delta}=\sqrt{36420}=\sqrt{4*9105}=\sqrt{4}*\sqrt{9105}=2\sqrt{9105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-2\sqrt{9105}}{2*-40}=\frac{-190-2\sqrt{9105}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+2\sqrt{9105}}{2*-40}=\frac{-190+2\sqrt{9105}}{-80}
$