-1/4x+2=4x-15

Solution for -1/4x+2=4x-15 equation:

-1/4x+2=4x-15

We move all terms to the left:

-1/4x+2-(4x-15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x-4x+15+2=0

We multiply all the terms by the denominator


-4x*4x+15*4x+2*4x-1=0

Wy multiply elements

-16x^2+60x+8x-1=0

We add all the numbers together, and all the variables

-16x^2+68x-1=0

a = -16; b = 68; c = -1;
Δ = b2-4ac
Δ = 682-4·(-16)·(-1)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{285}}{2*-16}=\frac{-68-4\sqrt{285}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{285}}{2*-16}=\frac{-68+4\sqrt{285}}{-32}
$