1.5x2+12=0.5(5x2-8)

Solution for 1.5x2+12=0.5(5x2-8) equation:

1.5x^2+12=0.5(5x^2-8)

We move all terms to the left:

1.5x^2+12-(0.5(5x^2-8))=0


We calculate terms in parentheses: -(0.5(5x^2-8)), so:

0.5(5x^2-8)

We multiply parentheses

2.5x^2-4

Back to the equation:

-(2.5x^2-4)


We get rid of parentheses

1.5x^2-2.5x^2+4+12=0

We add all the numbers together, and all the variables

-1x^2+16=0

a = -1; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-1)·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-1}=\frac{8}{-2}
=-4
$