8x^2-9=40

Solution for 8x^2-9=40 equation:

8x^2-9=40

We move all terms to the left:

8x^2-9-(40)=0

We add all the numbers together, and all the variables

8x^2-49=0

a = 8; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·8·(-49)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*8}=\frac{0-28\sqrt{2}}{16}
=-\frac{28\sqrt{2}}{16}
=-\frac{7\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*8}=\frac{0+28\sqrt{2}}{16}
=\frac{28\sqrt{2}}{16}
=\frac{7\sqrt{2}}{4}
$