-14-5/4x=-3/8x-21

Solution for -14-5/4x=-3/8x-21 equation:

-14-5/4x=-3/8x-21

We move all terms to the left:

-14-5/4x-(-3/8x-21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-21)!=0

x∈R


We get rid of parentheses

-5/4x+3/8x+21-14=0

We calculate fractions


(-40x)/32x^2+12x/32x^2+21-14=0

We add all the numbers together, and all the variables

(-40x)/32x^2+12x/32x^2+7=0

We multiply all the terms by the denominator


(-40x)+12x+7*32x^2=0

We add all the numbers together, and all the variables

12x+(-40x)+7*32x^2=0

Wy multiply elements

224x^2+12x+(-40x)=0

We get rid of parentheses

224x^2+12x-40x=0

We add all the numbers together, and all the variables

224x^2-28x=0

a = 224; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·224·0
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*224}=\frac{0}{448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*224}=\frac{56}{448}
=1/8
$