1/2x+2.5=3x-10

Solution for 1/2x+2.5=3x-10 equation:

1/2x+2.5=3x-10

We move all terms to the left:

1/2x+2.5-(3x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3x+10+2.5=0

We multiply all the terms by the denominator


-3x*2x+10*2x+(2.5)*2x+1=0

We multiply parentheses

-3x*2x+10*2x+5x+1=0

Wy multiply elements

-6x^2+20x+5x+1=0

We add all the numbers together, and all the variables

-6x^2+25x+1=0

a = -6; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·(-6)·1
Δ = 649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{649}}{2*-6}=\frac{-25-\sqrt{649}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{649}}{2*-6}=\frac{-25+\sqrt{649}}{-12}
$