x=9/4x-6

Solution for x=9/4x-6 equation:

x=9/4x-6

We move all terms to the left:

x-(9/4x-6)=0


Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

x-9/4x+6=0

We multiply all the terms by the denominator


x*4x+6*4x-9=0

Wy multiply elements

4x^2+24x-9=0

a = 4; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·4·(-9)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{5}}{2*4}=\frac{-24-12\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{5}}{2*4}=\frac{-24+12\sqrt{5}}{8}
$