31/7*x=66

Solution for 31/7*x=66 equation:

31/7*x=66

We move all terms to the left:

31/7*x-(66)=0


Domain of the equation: 7*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-66*7*x+31=0

Wy multiply elements

-462x*x+31=0

Wy multiply elements

-462x^2+31=0

a = -462; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-462)·31
Δ = 57288
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:

$\sqrt{\Delta}=\sqrt{57288}=\sqrt{4*14322}=\sqrt{4}*\sqrt{14322}=2\sqrt{14322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14322}}{2*-462}=\frac{0-2\sqrt{14322}}{-924}
=-\frac{2\sqrt{14322}}{-924}
=-\frac{\sqrt{14322}}{-462}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14322}}{2*-462}=\frac{0+2\sqrt{14322}}{-924}
=\frac{2\sqrt{14322}}{-924}
=\frac{\sqrt{14322}}{-462}
$