1/2x+4(3x+5)=97.5

Solution for 1/2x+4(3x+5)=97.5 equation:

1/2x+4(3x+5)=97.5

We move all terms to the left:

1/2x+4(3x+5)-(97.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+4(3x+5)-97.5=0

We multiply parentheses

1/2x+12x+20-97.5=0

We multiply all the terms by the denominator


12x*2x+20*2x-(97.5)*2x+1=0

We multiply parentheses

12x*2x+20*2x-195x+1=0

Wy multiply elements

24x^2+40x-195x+1=0

We add all the numbers together, and all the variables

24x^2-155x+1=0

a = 24; b = -155; c = +1;
Δ = b2-4ac
Δ = -1552-4·24·1
Δ = 23929
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{-(-155)-\sqrt{23929}}{2*24}=\frac{155-\sqrt{23929}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+\sqrt{23929}}{2*24}=\frac{155+\sqrt{23929}}{48}
$