8x2=3(x2+15)

Solution for 8x2=3(x2+15) equation:

8x^2=3(x2+15)

We move all terms to the left:

8x^2-(3(x2+15))=0

We add all the numbers together, and all the variables

8x^2-(3(+x^2+15))=0


We calculate terms in parentheses: -(3(+x^2+15)), so:

3(+x^2+15)

We multiply parentheses

3x^2+45

Back to the equation:

-(3x^2+45)


We get rid of parentheses

8x^2-3x^2-45=0

We add all the numbers together, and all the variables

5x^2-45=0

a = 5; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·5·(-45)
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*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*5}=\frac{30}{10}
=3
$