0.25x+3/8x=5

Solution for 0.25x+3/8x=5 equation:

0.25x+3/8x=5

We move all terms to the left:

0.25x+3/8x-(5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


(0.25x)*8x-5*8x+3=0

We add all the numbers together, and all the variables

(+0.25x)*8x-5*8x+3=0

We multiply parentheses

0x^2-5*8x+3=0

Wy multiply elements

0x^2-40x+3=0

We add all the numbers together, and all the variables

x^2-40x+3=0

a = 1; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·1·3
Δ = 1588
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:

$\sqrt{\Delta}=\sqrt{1588}=\sqrt{4*397}=\sqrt{4}*\sqrt{397}=2\sqrt{397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{397}}{2*1}=\frac{40-2\sqrt{397}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{397}}{2*1}=\frac{40+2\sqrt{397}}{2}
$