0.25(x-8)=5/4x+6

Solution for 0.25(x-8)=5/4x+6 equation:

0.25(x-8)=5/4x+6

We move all terms to the left:

0.25(x-8)-(5/4x+6)=0


Domain of the equation: 4x+6)!=0

x∈R


We multiply parentheses

0.25x-(5/4x+6)-2=0

We get rid of parentheses

0.25x-5/4x-6-2=0

We multiply all the terms by the denominator


(0.25x)*4x-6*4x-2*4x-5=0

We add all the numbers together, and all the variables

(+0.25x)*4x-6*4x-2*4x-5=0

We multiply parentheses

0x^2-6*4x-2*4x-5=0

Wy multiply elements

0x^2-24x-8x-5=0

We add all the numbers together, and all the variables

x^2-32x-5=0

a = 1; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·1·(-5)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-6\sqrt{29}}{2*1}=\frac{32-6\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+6\sqrt{29}}{2*1}=\frac{32+6\sqrt{29}}{2}
$