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

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

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

We move all terms to the left:

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

We multiply parentheses

1/2x+6x+15-97.5=0

We multiply all the terms by the denominator


6x*2x+15*2x-(97.5)*2x+1=0

We multiply parentheses

6x*2x+15*2x-195x+1=0

Wy multiply elements

12x^2+30x-195x+1=0

We add all the numbers together, and all the variables

12x^2-165x+1=0

a = 12; b = -165; c = +1;
Δ = b2-4ac
Δ = -1652-4·12·1
Δ = 27177
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{-(-165)-\sqrt{27177}}{2*12}=\frac{165-\sqrt{27177}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-165)+\sqrt{27177}}{2*12}=\frac{165+\sqrt{27177}}{24}
$