7/20*x=100

Solution for 7/20*x=100 equation:

7/20*x=100

We move all terms to the left:

7/20*x-(100)=0


Domain of the equation: 20*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-100*20*x+7=0

Wy multiply elements

-2000x*x+7=0

Wy multiply elements

-2000x^2+7=0

a = -2000; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2000)·7
Δ = 56000
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:

$\sqrt{\Delta}=\sqrt{56000}=\sqrt{1600*35}=\sqrt{1600}*\sqrt{35}=40\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{35}}{2*-2000}=\frac{0-40\sqrt{35}}{-4000}
=-\frac{40\sqrt{35}}{-4000}
=-\frac{\sqrt{35}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{35}}{2*-2000}=\frac{0+40\sqrt{35}}{-4000}
=\frac{40\sqrt{35}}{-4000}
=\frac{\sqrt{35}}{-100}
$