71/2x=41/4x+25

Solution for 71/2x=41/4x+25 equation:

71/2x=41/4x+25

We move all terms to the left:

71/2x-(41/4x+25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+25)!=0

x∈R


We get rid of parentheses

71/2x-41/4x-25=0

We calculate fractions


284x/8x^2+(-82x)/8x^2-25=0

We multiply all the terms by the denominator


284x+(-82x)-25*8x^2=0

Wy multiply elements

-200x^2+284x+(-82x)=0

We get rid of parentheses

-200x^2+284x-82x=0

We add all the numbers together, and all the variables

-200x^2+202x=0

a = -200; b = 202; c = 0;
Δ = b2-4ac
Δ = 2022-4·(-200)·0
Δ = 40804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40804}=202$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(202)-202}{2*-200}=\frac{-404}{-400}
=1+1/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(202)+202}{2*-200}=\frac{0}{-400}
=0
$