0.25x+2=5/8x-5

Solution for 0.25x+2=5/8x-5 equation:

0.25x+2=5/8x-5

We move all terms to the left:

0.25x+2-(5/8x-5)=0


Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

0.25x-5/8x+5+2=0

We multiply all the terms by the denominator


(0.25x)*8x+5*8x+2*8x-5=0

We add all the numbers together, and all the variables

(+0.25x)*8x+5*8x+2*8x-5=0

We multiply parentheses

0x^2+5*8x+2*8x-5=0

Wy multiply elements

0x^2+40x+16x-5=0

We add all the numbers together, and all the variables

x^2+56x-5=0

a = 1; b = 56; c = -5;
Δ = b2-4ac
Δ = 562-4·1·(-5)
Δ = 3156
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:

$\sqrt{\Delta}=\sqrt{3156}=\sqrt{4*789}=\sqrt{4}*\sqrt{789}=2\sqrt{789}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{789}}{2*1}=\frac{-56-2\sqrt{789}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{789}}{2*1}=\frac{-56+2\sqrt{789}}{2}
$