5-1/4x=5/8x+9

Solution for 5-1/4x=5/8x+9 equation:

5-1/4x=5/8x+9

We move all terms to the left:

5-1/4x-(5/8x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+9)!=0

x∈R


We get rid of parentheses

-1/4x-5/8x-9+5=0

We calculate fractions


(-8x)/32x^2+(-20x)/32x^2-9+5=0

We add all the numbers together, and all the variables

(-8x)/32x^2+(-20x)/32x^2-4=0

We multiply all the terms by the denominator


(-8x)+(-20x)-4*32x^2=0

Wy multiply elements

-128x^2+(-8x)+(-20x)=0

We get rid of parentheses

-128x^2-8x-20x=0

We add all the numbers together, and all the variables

-128x^2-28x=0

a = -128; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-128)·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*-128}=\frac{0}{-256}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-128}=\frac{56}{-256}
=-7/32
$