7/4x+7/4x+x+x=66

Solution for 7/4x+7/4x+x+x=66 equation:

7/4x+7/4x+x+x=66

We move all terms to the left:

7/4x+7/4x+x+x-(66)=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+7/4x+7/4x-66=0

We multiply all the terms by the denominator


2x*4x-66*4x+7+7=0

We add all the numbers together, and all the variables

2x*4x-66*4x+14=0

Wy multiply elements

8x^2-264x+14=0

a = 8; b = -264; c = +14;
Δ = b2-4ac
Δ = -2642-4·8·14
Δ = 69248
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:

$\sqrt{\Delta}=\sqrt{69248}=\sqrt{64*1082}=\sqrt{64}*\sqrt{1082}=8\sqrt{1082}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-8\sqrt{1082}}{2*8}=\frac{264-8\sqrt{1082}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+8\sqrt{1082}}{2*8}=\frac{264+8\sqrt{1082}}{16}
$