3/4x+1x=840

Solution for 3/4x+1x=840 equation:

3/4x+1x=840

We move all terms to the left:

3/4x+1x-(840)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-840=0

We multiply all the terms by the denominator


x*4x-840*4x+3=0

Wy multiply elements

4x^2-3360x+3=0

a = 4; b = -3360; c = +3;
Δ = b2-4ac
Δ = -33602-4·4·3
Δ = 11289552
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:

$\sqrt{\Delta}=\sqrt{11289552}=\sqrt{16*705597}=\sqrt{16}*\sqrt{705597}=4\sqrt{705597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3360)-4\sqrt{705597}}{2*4}=\frac{3360-4\sqrt{705597}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3360)+4\sqrt{705597}}{2*4}=\frac{3360+4\sqrt{705597}}{8}
$