5x=(5x+12)+(3x)/2

Solution for 5x=(5x+12)+(3x)/2 equation:

5x=(5x+12)+(3x)/2

We move all terms to the left:

5x-((5x+12)+(3x)/2)=0

We multiply all the terms by the denominator


5x*2)-((5x+12)+3x=0

We add all the numbers together, and all the variables

3x+5x*2)-((5x+12)=0

Wy multiply elements

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