X+(3/4g+30)=478

Solution for X+(3/4g+30)=478 equation:

X+(3/4X+30)=478

We move all terms to the left:

X+(3/4X+30)-(478)=0


Domain of the equation: 4X+30)!=0

X∈R


We get rid of parentheses

X+3/4X+30-478=0

We multiply all the terms by the denominator


X*4X+30*4X-478*4X+3=0

Wy multiply elements

4X^2+120X-1912X+3=0

We add all the numbers together, and all the variables

4X^2-1792X+3=0

a = 4; b = -1792; c = +3;
Δ = b2-4ac
Δ = -17922-4·4·3
Δ = 3211216
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:

$\sqrt{\Delta}=\sqrt{3211216}=\sqrt{16*200701}=\sqrt{16}*\sqrt{200701}=4\sqrt{200701}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1792)-4\sqrt{200701}}{2*4}=\frac{1792-4\sqrt{200701}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1792)+4\sqrt{200701}}{2*4}=\frac{1792+4\sqrt{200701}}{8}
$