8x-20+1/2x+25=180

Solution for 8x-20+1/2x+25=180 equation:

8x-20+1/2x+25=180

We move all terms to the left:

8x-20+1/2x+25-(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

8x+1/2x-175=0

We multiply all the terms by the denominator


8x*2x-175*2x+1=0

Wy multiply elements

16x^2-350x+1=0

a = 16; b = -350; c = +1;
Δ = b2-4ac
Δ = -3502-4·16·1
Δ = 122436
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:

$\sqrt{\Delta}=\sqrt{122436}=\sqrt{36*3401}=\sqrt{36}*\sqrt{3401}=6\sqrt{3401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-6\sqrt{3401}}{2*16}=\frac{350-6\sqrt{3401}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+6\sqrt{3401}}{2*16}=\frac{350+6\sqrt{3401}}{32}
$