3/4x+3/4x+x+x=420

Solution for 3/4x+3/4x+x+x=420 equation:

3/4x+3/4x+x+x=420

We move all terms to the left:

3/4x+3/4x+x+x-(420)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x+3/4x-420=0

We multiply all the terms by the denominator


2x*4x-420*4x+3+3=0

We add all the numbers together, and all the variables

2x*4x-420*4x+6=0

Wy multiply elements

8x^2-1680x+6=0

a = 8; b = -1680; c = +6;
Δ = b2-4ac
Δ = -16802-4·8·6
Δ = 2822208
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:

$\sqrt{\Delta}=\sqrt{2822208}=\sqrt{64*44097}=\sqrt{64}*\sqrt{44097}=8\sqrt{44097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1680)-8\sqrt{44097}}{2*8}=\frac{1680-8\sqrt{44097}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1680)+8\sqrt{44097}}{2*8}=\frac{1680+8\sqrt{44097}}{16}
$