(5/6)x=75

Solution for (5/6)x=75 equation:

(5/6)x=75

We move all terms to the left:

(5/6)x-(75)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)x-75=0

We multiply parentheses

5x^2-75=0

a = 5; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·5·(-75)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*5}=\frac{0-10\sqrt{15}}{10}
=-\frac{10\sqrt{15}}{10}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*5}=\frac{0+10\sqrt{15}}{10}
=\frac{10\sqrt{15}}{10}
=\sqrt{15}
$