3/2x+4x=415

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Solution for 3/2x+4x=415 equation: 



3/2x+4x=415

We move all terms to the left:

3/2x+4x-(415)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

4x+3/2x-415=0

We multiply all the terms by the denominator


4x*2x-415*2x+3=0

Wy multiply elements

8x^2-830x+3=0

a = 8; b = -830; c = +3;
Δ = b2-4ac
Δ = -8302-4·8·3
Δ = 688804
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:


$\sqrt{\Delta}=\sqrt{688804}=\sqrt{4*172201}=\sqrt{4}*\sqrt{172201}=2\sqrt{172201}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-830)-2\sqrt{172201}}{2*8}=\frac{830-2\sqrt{172201}}{16}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-830)+2\sqrt{172201}}{2*8}=\frac{830+2\sqrt{172201}}{16}
$

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