-7x+(420/2x)=3222

Solution for -7x+(420/2x)=3222 equation:

-7x+(420/2x)=3222

We move all terms to the left:

-7x+(420/2x)-(3222)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+(+420/2x)-3222=0

We get rid of parentheses

-7x+420/2x-3222=0

We multiply all the terms by the denominator


-7x*2x-3222*2x+420=0

Wy multiply elements

-14x^2-6444x+420=0

a = -14; b = -6444; c = +420;
Δ = b2-4ac
Δ = -64442-4·(-14)·420
Δ = 41548656
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:

$\sqrt{\Delta}=\sqrt{41548656}=\sqrt{16*2596791}=\sqrt{16}*\sqrt{2596791}=4\sqrt{2596791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6444)-4\sqrt{2596791}}{2*-14}=\frac{6444-4\sqrt{2596791}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6444)+4\sqrt{2596791}}{2*-14}=\frac{6444+4\sqrt{2596791}}{-28}
$