(22/15)x=x+77

Solution for (22/15)x=x+77 equation:

(22/15)x=x+77

We move all terms to the left:

(22/15)x-(x+77)=0


Domain of the equation: 15)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+22/15)x-(x+77)=0

We multiply parentheses

22x^2-(x+77)=0

We get rid of parentheses

22x^2-x-77=0

We add all the numbers together, and all the variables

22x^2-1x-77=0

a = 22; b = -1; c = -77;
Δ = b2-4ac
Δ = -12-4·22·(-77)
Δ = 6777
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:

$\sqrt{\Delta}=\sqrt{6777}=\sqrt{9*753}=\sqrt{9}*\sqrt{753}=3\sqrt{753}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{753}}{2*22}=\frac{1-3\sqrt{753}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{753}}{2*22}=\frac{1+3\sqrt{753}}{44}
$