(8x^2+24x)=(-4x^2+15)

Solution for (8x^2+24x)=(-4x^2+15) equation:

(8x^2+24x)=(-4x^2+15)

We move all terms to the left:

(8x^2+24x)-((-4x^2+15))=0

We get rid of parentheses

-((-4x^2+15))+8x^2+24x=0


We calculate terms in parentheses: -((-4x^2+15)), so:

(-4x^2+15)

We get rid of parentheses

-4x^2+15

Back to the equation:

-(-4x^2+15)


We add all the numbers together, and all the variables

8x^2-(-4x^2+15)+24x=0

We get rid of parentheses

8x^2+4x^2+24x-15=0

We add all the numbers together, and all the variables

12x^2+24x-15=0

a = 12; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·12·(-15)
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{-(24)-36}{2*12}=\frac{-60}{24}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+36}{2*12}=\frac{12}{24}
=1/2
$