420=7/6*x

Solution for 420=7/6*x equation:

420=7/6*x

We move all terms to the left:

420-(7/6*x)=0


Domain of the equation: 6*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+7/6*x)+420=0

We get rid of parentheses

-7/6*x+420=0

We multiply all the terms by the denominator


420*6*x-7=0

Wy multiply elements

2520x*x-7=0

Wy multiply elements

2520x^2-7=0

a = 2520; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·2520·(-7)
Δ = 70560
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:

$\sqrt{\Delta}=\sqrt{70560}=\sqrt{7056*10}=\sqrt{7056}*\sqrt{10}=84\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{10}}{2*2520}=\frac{0-84\sqrt{10}}{5040}
=-\frac{84\sqrt{10}}{5040}
=-\frac{\sqrt{10}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{10}}{2*2520}=\frac{0+84\sqrt{10}}{5040}
=\frac{84\sqrt{10}}{5040}
=\frac{\sqrt{10}}{60}
$