(1/2)(10x-2)+3x=-25

Solution for (1/2)(10x-2)+3x=-25 equation:

(1/2)(10x-2)+3x=-25

We move all terms to the left:

(1/2)(10x-2)+3x-(-25)=0


Domain of the equation: 2)(10x-2)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(10x-2)+3x-(-25)=0

We add all the numbers together, and all the variables

3x+(+1/2)(10x-2)+25=0

We multiply parentheses ..

(+10x^2+1/2*-2)+3x+25=0

We multiply all the terms by the denominator


(+10x^2+1+3x*2*-2)+25*2*-2)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

16x^2-1=0

a = 16; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·16·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*16}=\frac{-8}{32}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*16}=\frac{8}{32}
=1/4
$