85/7*x=20

Solution for 85/7*x=20 equation:

85/7*x=20

We move all terms to the left:

85/7*x-(20)=0


Domain of the equation: 7*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-20*7*x+85=0

Wy multiply elements

-140x*x+85=0

Wy multiply elements

-140x^2+85=0

a = -140; b = 0; c = +85;
Δ = b2-4ac
Δ = 02-4·(-140)·85
Δ = 47600
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:

$\sqrt{\Delta}=\sqrt{47600}=\sqrt{400*119}=\sqrt{400}*\sqrt{119}=20\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{119}}{2*-140}=\frac{0-20\sqrt{119}}{-280}
=-\frac{20\sqrt{119}}{-280}
=-\frac{\sqrt{119}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{119}}{2*-140}=\frac{0+20\sqrt{119}}{-280}
=\frac{20\sqrt{119}}{-280}
=\frac{\sqrt{119}}{-14}
$