(-3x^2/2)+1=-53

Solution for (-3x^2/2)+1=-53 equation:

(-3x^2/2)+1=-53

We move all terms to the left:

(-3x^2/2)+1-(-53)=0

We add all the numbers together, and all the variables

(-3x^2/2)+54=0

We get rid of parentheses

-3x^2/2+54=0

We multiply all the terms by the denominator


-3x^2+54*2=0

We add all the numbers together, and all the variables

-3x^2+108=0

a = -3; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-3)·108
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*-3}=\frac{36}{-6}
=-6
$