1/4x-10x=15

Solution for 1/4x-10x=15 equation:

1/4x-10x=15

We move all terms to the left:

1/4x-10x-(15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+1/4x-15=0

We multiply all the terms by the denominator


-10x*4x-15*4x+1=0

Wy multiply elements

-40x^2-60x+1=0

a = -40; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·(-40)·1
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{235}}{2*-40}=\frac{60-4\sqrt{235}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{235}}{2*-40}=\frac{60+4\sqrt{235}}{-80}
$