7.25x=3/4x+9

Solution for 7.25x=3/4x+9 equation:

7.25x=3/4x+9

We move all terms to the left:

7.25x-(3/4x+9)=0


Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

7.25x-3/4x-9=0

We multiply all the terms by the denominator


(7.25x)*4x-9*4x-3=0

We add all the numbers together, and all the variables

(+7.25x)*4x-9*4x-3=0

We multiply parentheses

28x^2-9*4x-3=0

Wy multiply elements

28x^2-36x-3=0

a = 28; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·28·(-3)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{102}}{2*28}=\frac{36-4\sqrt{102}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{102}}{2*28}=\frac{36+4\sqrt{102}}{56}
$