(-3)=2(4x2-5)-15

Solution for (-3)=2(4x2-5)-15 equation:

(-3)=2(4x^2-5)-15

We move all terms to the left:

(-3)-(2(4x^2-5)-15)=0

We add all the numbers together, and all the variables

-(2(4x^2-5)-15)-3=0


We calculate terms in parentheses: -(2(4x^2-5)-15), so:

2(4x^2-5)-15

We multiply parentheses

8x^2-10-15

We add all the numbers together, and all the variables

8x^2-25

Back to the equation:

-(8x^2-25)


We get rid of parentheses

-8x^2+25-3=0

We add all the numbers together, and all the variables

-8x^2+22=0

a = -8; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-8)·22
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*-8}=\frac{0-8\sqrt{11}}{-16}
=-\frac{8\sqrt{11}}{-16}
=-\frac{\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*-8}=\frac{0+8\sqrt{11}}{-16}
=\frac{8\sqrt{11}}{-16}
=\frac{\sqrt{11}}{-2}
$