-1/2x+3=5x+25

Solution for -1/2x+3=5x+25 equation:

-1/2x+3=5x+25

We move all terms to the left:

-1/2x+3-(5x+25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-5x-25+3=0

We multiply all the terms by the denominator


-5x*2x-25*2x+3*2x-1=0

Wy multiply elements

-10x^2-50x+6x-1=0

We add all the numbers together, and all the variables

-10x^2-44x-1=0

a = -10; b = -44; c = -1;
Δ = b2-4ac
Δ = -442-4·(-10)·(-1)
Δ = 1896
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:

$\sqrt{\Delta}=\sqrt{1896}=\sqrt{4*474}=\sqrt{4}*\sqrt{474}=2\sqrt{474}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{474}}{2*-10}=\frac{44-2\sqrt{474}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{474}}{2*-10}=\frac{44+2\sqrt{474}}{-20}
$