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x+3/4x+3/4x=180
We move all terms to the left:
x+3/4x+3/4x-(180)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
x*4x-180*4x+3+3=0
We add all the numbers together, and all the variables
x*4x-180*4x+6=0
Wy multiply elements
4x^2-720x+6=0
a = 4; b = -720; c = +6;
Δ = b2-4ac
Δ = -7202-4·4·6
Δ = 518304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{518304}=\sqrt{16*32394}=\sqrt{16}*\sqrt{32394}=4\sqrt{32394}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32394}}{2*4}=\frac{720-4\sqrt{32394}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32394}}{2*4}=\frac{720+4\sqrt{32394}}{8} $
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