3/4x+100-20=7x+800

Solution for 3/4x+100-20=7x+800 equation:

3/4x+100-20=7x+800

We move all terms to the left:

3/4x+100-20-(7x+800)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(7x+800)+80=0

We get rid of parentheses

3/4x-7x-800+80=0

We multiply all the terms by the denominator


-7x*4x-800*4x+80*4x+3=0

Wy multiply elements

-28x^2-3200x+320x+3=0

We add all the numbers together, and all the variables

-28x^2-2880x+3=0

a = -28; b = -2880; c = +3;
Δ = b2-4ac
Δ = -28802-4·(-28)·3
Δ = 8294736
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:

$\sqrt{\Delta}=\sqrt{8294736}=\sqrt{16*518421}=\sqrt{16}*\sqrt{518421}=4\sqrt{518421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2880)-4\sqrt{518421}}{2*-28}=\frac{2880-4\sqrt{518421}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2880)+4\sqrt{518421}}{2*-28}=\frac{2880+4\sqrt{518421}}{-56}
$