12=3/2x2-(4)(7)

Solution for 12=3/2x2-(4)(7) equation:

12=3/2x^2-(4)(7)

We move all terms to the left:

12-(3/2x^2-(4)(7))=0


Domain of the equation: 2x^2-47)!=0

x∈R


We get rid of parentheses

-3/2x^2+47+12=0

We multiply all the terms by the denominator


47*2x^2+12*2x^2-3=0

Wy multiply elements

94x^2+24x^2-3=0

We add all the numbers together, and all the variables

118x^2-3=0

a = 118; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·118·(-3)
Δ = 1416
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:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{354}}{2*118}=\frac{0-2\sqrt{354}}{236}
=-\frac{2\sqrt{354}}{236}
=-\frac{\sqrt{354}}{118}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{354}}{2*118}=\frac{0+2\sqrt{354}}{236}
=\frac{2\sqrt{354}}{236}
=\frac{\sqrt{354}}{118}
$