3x^2/2+14=5x^2

Solution for 3x^2/2+14=5x^2 equation:

3x^2/2+14=5x^2

We move all terms to the left:

3x^2/2+14-(5x^2)=0

We add all the numbers together, and all the variables

-5x^2+3x^2/2+14=0

We multiply all the terms by the denominator


3x^2-5x^2*2+14*2=0

We add all the numbers together, and all the variables

3x^2-5x^2*2+28=0

Wy multiply elements

3x^2-10x^2+28=0

We add all the numbers together, and all the variables

-7x^2+28=0

a = -7; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-7)·28
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*-7}=\frac{-28}{-14}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*-7}=\frac{28}{-14}
=-2
$