10x+3/2x=180

Solution for 10x+3/2x=180 equation:

10x+3/2x=180

We move all terms to the left:

10x+3/2x-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


10x*2x-180*2x+3=0

Wy multiply elements

20x^2-360x+3=0

a = 20; b = -360; c = +3;
Δ = b2-4ac
Δ = -3602-4·20·3
Δ = 129360
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:

$\sqrt{\Delta}=\sqrt{129360}=\sqrt{784*165}=\sqrt{784}*\sqrt{165}=28\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-28\sqrt{165}}{2*20}=\frac{360-28\sqrt{165}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+28\sqrt{165}}{2*20}=\frac{360+28\sqrt{165}}{40}
$