-4x+12.5=1/4x+4

Solution for -4x+12.5=1/4x+4 equation:

-4x+12.5=1/4x+4

We move all terms to the left:

-4x+12.5-(1/4x+4)=0


Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

-4x-1/4x-4+12.5=0

We multiply all the terms by the denominator


-4x*4x-4*4x+(12.5)*4x-1=0

We multiply parentheses

-4x*4x-4*4x+50x-1=0

Wy multiply elements

-16x^2-16x+50x-1=0

We add all the numbers together, and all the variables

-16x^2+34x-1=0

a = -16; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·(-16)·(-1)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{273}}{2*-16}=\frac{-34-2\sqrt{273}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{273}}{2*-16}=\frac{-34+2\sqrt{273}}{-32}
$