1/4x+5=4x-7

Solution for 1/4x+5=4x-7 equation:

1/4x+5=4x-7

We move all terms to the left:

1/4x+5-(4x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-4x+7+5=0

We multiply all the terms by the denominator


-4x*4x+7*4x+5*4x+1=0

Wy multiply elements

-16x^2+28x+20x+1=0

We add all the numbers together, and all the variables

-16x^2+48x+1=0

a = -16; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-16)·1
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{37}}{2*-16}=\frac{-48-8\sqrt{37}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{37}}{2*-16}=\frac{-48+8\sqrt{37}}{-32}
$