9(5-3x)=1/2x+4

Solution for 9(5-3x)=1/2x+4 equation:

9(5-3x)=1/2x+4

We move all terms to the left:

9(5-3x)-(1/2x+4)=0


Domain of the equation: 2x+4)!=0

x∈R


We add all the numbers together, and all the variables

9(-3x+5)-(1/2x+4)=0

We multiply parentheses

-27x-(1/2x+4)+45=0

We get rid of parentheses

-27x-1/2x-4+45=0

We multiply all the terms by the denominator


-27x*2x-4*2x+45*2x-1=0

Wy multiply elements

-54x^2-8x+90x-1=0

We add all the numbers together, and all the variables

-54x^2+82x-1=0

a = -54; b = 82; c = -1;
Δ = b2-4ac
Δ = 822-4·(-54)·(-1)
Δ = 6508
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6508}=\sqrt{4*1627}=\sqrt{4}*\sqrt{1627}=2\sqrt{1627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{1627}}{2*-54}=\frac{-82-2\sqrt{1627}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{1627}}{2*-54}=\frac{-82+2\sqrt{1627}}{-108}
$