(1/2)5x+8=3x+12

Solution for (1/2)5x+8=3x+12 equation:

(1/2)5x+8=3x+12

We move all terms to the left:

(1/2)5x+8-(3x+12)=0


Domain of the equation: 2)5x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)5x-(3x+12)+8=0

We multiply parentheses

5x^2-(3x+12)+8=0

We get rid of parentheses

5x^2-3x-12+8=0

We add all the numbers together, and all the variables

5x^2-3x-4=0

a = 5; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·5·(-4)
Δ = 89
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{-(-3)-\sqrt{89}}{2*5}=\frac{3-\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*5}=\frac{3+\sqrt{89}}{10}
$