(1/4)x+(3/8)x=5

Solution for (1/4)x+(3/8)x=5 equation:

(1/4)x+(3/8)x=5

We move all terms to the left:

(1/4)x+(3/8)x-(5)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)x+(+3/8)x-5=0

We multiply parentheses

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

We add all the numbers together, and all the variables

4x^2-5=0

a = 4; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·4·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*4}=\frac{0-4\sqrt{5}}{8}
=-\frac{4\sqrt{5}}{8}
=-\frac{\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*4}=\frac{0+4\sqrt{5}}{8}
=\frac{4\sqrt{5}}{8}
=\frac{\sqrt{5}}{2}
$