.25x+2=-5/8x-5

Solution for .25x+2=-5/8x-5 equation:

.25x+2=-5/8x-5

We move all terms to the left:

.25x+2-(-5/8x-5)=0


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

x∈R


We get rid of parentheses

.25x+5/8x+5+2=0

We multiply all the terms by the denominator


(.25x)*8x+5*8x+2*8x+5=0

We add all the numbers together, and all the variables

(+.25x)*8x+5*8x+2*8x+5=0

We multiply parentheses

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

Wy multiply elements

8x^2+40x+16x+5=0

We add all the numbers together, and all the variables

8x^2+56x+5=0

a = 8; b = 56; c = +5;
Δ = b2-4ac
Δ = 562-4·8·5
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{186}}{2*8}=\frac{-56-4\sqrt{186}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{186}}{2*8}=\frac{-56+4\sqrt{186}}{16}
$