4x+25=1/2x=45

Solution for 4x+25=1/2x=45 equation:

4x+25=1/2x=45

We move all terms to the left:

4x+25-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+1/2x)+25=0

We get rid of parentheses

4x-1/2x+25=0

We multiply all the terms by the denominator


4x*2x+25*2x-1=0

Wy multiply elements

8x^2+50x-1=0

a = 8; b = 50; c = -1;
Δ = b2-4ac
Δ = 502-4·8·(-1)
Δ = 2532
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:

$\sqrt{\Delta}=\sqrt{2532}=\sqrt{4*633}=\sqrt{4}*\sqrt{633}=2\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{633}}{2*8}=\frac{-50-2\sqrt{633}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{633}}{2*8}=\frac{-50+2\sqrt{633}}{16}
$