10x+3/2x=185

Solution for 10x+3/2x=185 equation:

10x+3/2x=185

We move all terms to the left:

10x+3/2x-(185)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x-185*2x+3=0

Wy multiply elements

20x^2-370x+3=0

a = 20; b = -370; c = +3;
Δ = b2-4ac
Δ = -3702-4·20·3
Δ = 136660
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:

$\sqrt{\Delta}=\sqrt{136660}=\sqrt{4*34165}=\sqrt{4}*\sqrt{34165}=2\sqrt{34165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-370)-2\sqrt{34165}}{2*20}=\frac{370-2\sqrt{34165}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-370)+2\sqrt{34165}}{2*20}=\frac{370+2\sqrt{34165}}{40}
$