22/15x=x+77

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

22/15x=x+77

We move all terms to the left:

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


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We get rid of parentheses

22/15x-x-77=0

We multiply all the terms by the denominator


-x*15x-77*15x+22=0

Wy multiply elements

-15x^2-1155x+22=0

a = -15; b = -1155; c = +22;
Δ = b2-4ac
Δ = -11552-4·(-15)·22
Δ = 1335345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1155)-\sqrt{1335345}}{2*-15}=\frac{1155-\sqrt{1335345}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1155)+\sqrt{1335345}}{2*-15}=\frac{1155+\sqrt{1335345}}{-30}
$