234-2=(3/2)(78-x)

Solution for 234-2=(3/2)(78-x) equation:

234-2=(3/2)(78-x)

We move all terms to the left:

234-2-((3/2)(78-x))=0


Domain of the equation: 2)(78-x))!=0

x∈R


We add all the numbers together, and all the variables

-((+3/2)(-1x+78))+234-2=0

We add all the numbers together, and all the variables

-((+3/2)(-1x+78))+232=0

We multiply parentheses ..

-((-3x^2+3/2*78))+232=0

We multiply all the terms by the denominator


-((-3x^2+3+232*2*78))=0


We calculate terms in parentheses: -((-3x^2+3+232*2*78)), so:

(-3x^2+3+232*2*78)

We get rid of parentheses

-3x^2+3+232*2*78

We add all the numbers together, and all the variables

-3x^2+36195

Back to the equation:

-(-3x^2+36195)


We get rid of parentheses

3x^2-36195=0

a = 3; b = 0; c = -36195;
Δ = b2-4ac
Δ = 02-4·3·(-36195)
Δ = 434340
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:

$\sqrt{\Delta}=\sqrt{434340}=\sqrt{36*12065}=\sqrt{36}*\sqrt{12065}=6\sqrt{12065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{12065}}{2*3}=\frac{0-6\sqrt{12065}}{6}
=-\frac{6\sqrt{12065}}{6}
=-\sqrt{12065}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{12065}}{2*3}=\frac{0+6\sqrt{12065}}{6}
=\frac{6\sqrt{12065}}{6}
=\sqrt{12065}
$