1/8x+3/4x=21

Solution for 1/8x+3/4x=21 equation:

1/8x+3/4x=21

We move all terms to the left:

1/8x+3/4x-(21)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/32x^2+24x/32x^2-21=0

We multiply all the terms by the denominator


4x+24x-21*32x^2=0

We add all the numbers together, and all the variables

28x-21*32x^2=0

Wy multiply elements

-672x^2+28x=0

a = -672; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-672)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-672}=\frac{-56}{-1344}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-672}=\frac{0}{-1344}
=0
$