14x^2-18.5=8x^2+19

Solution for 14x^2-18.5=8x^2+19 equation:

14x^2-18.5=8x^2+19

We move all terms to the left:

14x^2-18.5-(8x^2+19)=0

We get rid of parentheses

14x^2-8x^2-19-18.5=0

We add all the numbers together, and all the variables

6x^2-37.5=0

a = 6; b = 0; c = -37.5;
Δ = b2-4ac
Δ = 02-4·6·(-37.5)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*6}=\frac{30}{12}
=2+1/2
$