3(x/2+5)=3/4x+11

Solution for 3(x/2+5)=3/4x+11 equation:

3(x/2+5)=3/4x+11

We move all terms to the left:

3(x/2+5)-(3/4x+11)=0


Domain of the equation: 4x+11)!=0

x∈R


We multiply parentheses

3x-(3/4x+11)+15=0

We get rid of parentheses

3x-3/4x-11+15=0

We multiply all the terms by the denominator


3x*4x-11*4x+15*4x-3=0

Wy multiply elements

12x^2-44x+60x-3=0

We add all the numbers together, and all the variables

12x^2+16x-3=0

a = 12; b = 16; c = -3;
Δ = b2-4ac
Δ = 162-4·12·(-3)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*12}=\frac{4}{24}
=1/6
$