8/5X-68=y

Solution for 8/5X-68=y equation:

8/5X-68=X

We move all terms to the left:

8/5X-68-(X)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We add all the numbers together, and all the variables

-1X+8/5X-68=0

We multiply all the terms by the denominator


-1X*5X-68*5X+8=0

Wy multiply elements

-5X^2-340X+8=0

a = -5; b = -340; c = +8;
Δ = b2-4ac
Δ = -3402-4·(-5)·8
Δ = 115760
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:

$\sqrt{\Delta}=\sqrt{115760}=\sqrt{16*7235}=\sqrt{16}*\sqrt{7235}=4\sqrt{7235}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-4\sqrt{7235}}{2*-5}=\frac{340-4\sqrt{7235}}{-10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+4\sqrt{7235}}{2*-5}=\frac{340+4\sqrt{7235}}{-10}
$