10x+3/2x+5=180

Solution for 10x+3/2x+5=180 equation:

10x+3/2x+5=180

We move all terms to the left:

10x+3/2x+5-(180)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

10x+3/2x-175=0

We multiply all the terms by the denominator


10x*2x-175*2x+3=0

Wy multiply elements

20x^2-350x+3=0

a = 20; b = -350; c = +3;
Δ = b2-4ac
Δ = -3502-4·20·3
Δ = 122260
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:

$\sqrt{\Delta}=\sqrt{122260}=\sqrt{4*30565}=\sqrt{4}*\sqrt{30565}=2\sqrt{30565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30565}}{2*20}=\frac{350-2\sqrt{30565}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30565}}{2*20}=\frac{350+2\sqrt{30565}}{40}
$