X-6=7/9x+10

Solution for X-6=7/9x+10 equation:

X-6=7/9X+10

We move all terms to the left:

X-6-(7/9X+10)=0


Domain of the equation: 9X+10)!=0

X∈R


We get rid of parentheses

X-7/9X-10-6=0

We multiply all the terms by the denominator


X*9X-10*9X-6*9X-7=0

Wy multiply elements

9X^2-90X-54X-7=0

We add all the numbers together, and all the variables

9X^2-144X-7=0

a = 9; b = -144; c = -7;
Δ = b2-4ac
Δ = -1442-4·9·(-7)
Δ = 20988
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:

$\sqrt{\Delta}=\sqrt{20988}=\sqrt{36*583}=\sqrt{36}*\sqrt{583}=6\sqrt{583}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-6\sqrt{583}}{2*9}=\frac{144-6\sqrt{583}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+6\sqrt{583}}{2*9}=\frac{144+6\sqrt{583}}{18}
$