8x-20=1/2x+25

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

8x-20=1/2x+25

We move all terms to the left:

8x-20-(1/2x+25)=0


Domain of the equation: 2x+25)!=0

x∈R


We get rid of parentheses

8x-1/2x-25-20=0

We multiply all the terms by the denominator


8x*2x-25*2x-20*2x-1=0

Wy multiply elements

16x^2-50x-40x-1=0

We add all the numbers together, and all the variables

16x^2-90x-1=0

a = 16; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·16·(-1)
Δ = 8164
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:

$\sqrt{\Delta}=\sqrt{8164}=\sqrt{4*2041}=\sqrt{4}*\sqrt{2041}=2\sqrt{2041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2041}}{2*16}=\frac{90-2\sqrt{2041}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2041}}{2*16}=\frac{90+2\sqrt{2041}}{32}
$