x+3+4(x-13)+3/4x=66

Solution for x+3+4(x-13)+3/4x=66 equation:

x+3+4(x-13)+3/4x=66

We move all terms to the left:

x+3+4(x-13)+3/4x-(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

x+4(x-13)+3/4x-63=0

We multiply parentheses

x+4x+3/4x-52-63=0

We multiply all the terms by the denominator


x*4x+4x*4x-52*4x-63*4x+3=0

Wy multiply elements

4x^2+16x^2-208x-252x+3=0

We add all the numbers together, and all the variables

20x^2-460x+3=0

a = 20; b = -460; c = +3;
Δ = b2-4ac
Δ = -4602-4·20·3
Δ = 211360
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:

$\sqrt{\Delta}=\sqrt{211360}=\sqrt{16*13210}=\sqrt{16}*\sqrt{13210}=4\sqrt{13210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-4\sqrt{13210}}{2*20}=\frac{460-4\sqrt{13210}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+4\sqrt{13210}}{2*20}=\frac{460+4\sqrt{13210}}{40}
$