1/2x+50=2x-15

Solution for 1/2x+50=2x-15 equation:

1/2x+50=2x-15

We move all terms to the left:

1/2x+50-(2x-15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x+15+50=0

We multiply all the terms by the denominator


-2x*2x+15*2x+50*2x+1=0

Wy multiply elements

-4x^2+30x+100x+1=0

We add all the numbers together, and all the variables

-4x^2+130x+1=0

a = -4; b = 130; c = +1;
Δ = b2-4ac
Δ = 1302-4·(-4)·1
Δ = 16916
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:

$\sqrt{\Delta}=\sqrt{16916}=\sqrt{4*4229}=\sqrt{4}*\sqrt{4229}=2\sqrt{4229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{4229}}{2*-4}=\frac{-130-2\sqrt{4229}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{4229}}{2*-4}=\frac{-130+2\sqrt{4229}}{-8}
$