(5/6)x=2+7/10

Solution for (5/6)x=2+7/10 equation:

(5/6)x=2+7/10

We move all terms to the left:

(5/6)x-(2+7/10)=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-(7/10+2)=0

We multiply parentheses

5x^2-(7/10+2)=0

We get rid of parentheses

5x^2-2-7/10=0

We multiply all the terms by the denominator


5x^2*10-7-2*10=0

We add all the numbers together, and all the variables

5x^2*10-27=0

Wy multiply elements

50x^2-27=0

a = 50; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·50·(-27)
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{6}}{2*50}=\frac{0-30\sqrt{6}}{100}
=-\frac{30\sqrt{6}}{100}
=-\frac{3\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{6}}{2*50}=\frac{0+30\sqrt{6}}{100}
=\frac{30\sqrt{6}}{100}
=\frac{3\sqrt{6}}{10}
$