x+3/4x=455

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Solution for x+3/4x=455 equation: 



x+3/4x=455

We move all terms to the left:

x+3/4x-(455)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We multiply all the terms by the denominator


x*4x-455*4x+3=0

Wy multiply elements

4x^2-1820x+3=0

a = 4; b = -1820; c = +3;
Δ = b2-4ac
Δ = -18202-4·4·3
Δ = 3312352
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:


$\sqrt{\Delta}=\sqrt{3312352}=\sqrt{16*207022}=\sqrt{16}*\sqrt{207022}=4\sqrt{207022}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1820)-4\sqrt{207022}}{2*4}=\frac{1820-4\sqrt{207022}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1820)+4\sqrt{207022}}{2*4}=\frac{1820+4\sqrt{207022}}{8}
$

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