7/15*x=140

Solution for 7/15*x=140 equation:

7/15*x=140

We move all terms to the left:

7/15*x-(140)=0


Domain of the equation: 15*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-140*15*x+7=0

Wy multiply elements

-2100x*x+7=0

Wy multiply elements

-2100x^2+7=0

a = -2100; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2100)·7
Δ = 58800
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:

$\sqrt{\Delta}=\sqrt{58800}=\sqrt{19600*3}=\sqrt{19600}*\sqrt{3}=140\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140\sqrt{3}}{2*-2100}=\frac{0-140\sqrt{3}}{-4200}
=-\frac{140\sqrt{3}}{-4200}
=-\frac{\sqrt{3}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140\sqrt{3}}{2*-2100}=\frac{0+140\sqrt{3}}{-4200}
=\frac{140\sqrt{3}}{-4200}
=\frac{\sqrt{3}}{-30}
$