5x-4+3/2x+21=180

Solution for 5x-4+3/2x+21=180 equation:

5x-4+3/2x+21=180

We move all terms to the left:

5x-4+3/2x+21-(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

5x+3/2x-163=0

We multiply all the terms by the denominator


5x*2x-163*2x+3=0

Wy multiply elements

10x^2-326x+3=0

a = 10; b = -326; c = +3;
Δ = b2-4ac
Δ = -3262-4·10·3
Δ = 106156
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:

$\sqrt{\Delta}=\sqrt{106156}=\sqrt{4*26539}=\sqrt{4}*\sqrt{26539}=2\sqrt{26539}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-326)-2\sqrt{26539}}{2*10}=\frac{326-2\sqrt{26539}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-326)+2\sqrt{26539}}{2*10}=\frac{326+2\sqrt{26539}}{20}
$