X-6=5/6x+4

Solution for X-6=5/6x+4 equation:

X-6=5/6X+4

We move all terms to the left:

X-6-(5/6X+4)=0


Domain of the equation: 6X+4)!=0

X∈R


We get rid of parentheses

X-5/6X-4-6=0

We multiply all the terms by the denominator


X*6X-4*6X-6*6X-5=0

Wy multiply elements

6X^2-24X-36X-5=0

We add all the numbers together, and all the variables

6X^2-60X-5=0

a = 6; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·6·(-5)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{930}}{2*6}=\frac{60-2\sqrt{930}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{930}}{2*6}=\frac{60+2\sqrt{930}}{12}
$