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

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

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

We move all terms to the left:

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


Domain of the equation: 2)(10x-2)+3x)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -((+10x^2+1-25*2*-2)+3x), so:

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

We get rid of parentheses

10x^2+3x+1-2-25*2*

We add all the numbers together, and all the variables

10x^2+3x

Back to the equation:

-(10x^2+3x)


We get rid of parentheses

-10x^2-3x=0

a = -10; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-10)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-10}=\frac{6}{-20}
=-3/10
$