8.4/100*x=42

Solution for 8.4/100*x=42 equation:

8.4/100*x=42

We move all terms to the left:

8.4/100*x-(42)=0


Domain of the equation: 100*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-42*100*x+8.4=0

Wy multiply elements

-4200x*x+8.4=0

Wy multiply elements

-4200x^2+8.4=0

a = -4200; b = 0; c = +8.4;
Δ = b2-4ac
Δ = 02-4·(-4200)·8.4
Δ = 141120
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:

$\sqrt{\Delta}=\sqrt{141120}=\sqrt{28224*5}=\sqrt{28224}*\sqrt{5}=168\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-168\sqrt{5}}{2*-4200}=\frac{0-168\sqrt{5}}{-8400}
=-\frac{168\sqrt{5}}{-8400}
=-\frac{\sqrt{5}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+168\sqrt{5}}{2*-4200}=\frac{0+168\sqrt{5}}{-8400}
=\frac{168\sqrt{5}}{-8400}
=\frac{\sqrt{5}}{-50}
$