9x+2=(3/4)(2x+11)

Solution for 9x+2=(3/4)(2x+11) equation:

9x+2=(3/4)(2x+11)

We move all terms to the left:

9x+2-((3/4)(2x+11))=0


Domain of the equation: 4)(2x+11))!=0

x∈R


We add all the numbers together, and all the variables

9x-((+3/4)(2x+11))+2=0

We multiply parentheses ..

-((+6x^2+3/4*11))+9x+2=0

We multiply all the terms by the denominator


-((+6x^2+3+9x*4*11))+2*4*11))=0


We calculate terms in parentheses: -((+6x^2+3+9x*4*11)), so:

(+6x^2+3+9x*4*11)

We get rid of parentheses

6x^2+9x*4*11+3

Wy multiply elements

6x^2+396x*1+3

Wy multiply elements

6x^2+396x+3

Back to the equation:

-(6x^2+396x+3)


We add all the numbers together, and all the variables

-(6x^2+396x+3)=0

We get rid of parentheses

-6x^2-396x-3=0

a = -6; b = -396; c = -3;
Δ = b2-4ac
Δ = -3962-4·(-6)·(-3)
Δ = 156744
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:

$\sqrt{\Delta}=\sqrt{156744}=\sqrt{36*4354}=\sqrt{36}*\sqrt{4354}=6\sqrt{4354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-6\sqrt{4354}}{2*-6}=\frac{396-6\sqrt{4354}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+6\sqrt{4354}}{2*-6}=\frac{396+6\sqrt{4354}}{-12}
$