(x)=5/6x-4

Solution for (x)=5/6x-4 equation:

(x)=5/6x-4

We move all terms to the left:

(x)-(5/6x-4)=0


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

x∈R


We get rid of parentheses

x-5/6x+4=0

We multiply all the terms by the denominator


x*6x+4*6x-5=0

Wy multiply elements

6x^2+24x-5=0

a = 6; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·6·(-5)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{174}}{2*6}=\frac{-24-2\sqrt{174}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{174}}{2*6}=\frac{-24+2\sqrt{174}}{12}
$