51-12x=-8x^2+104

Solution for 51-12x=-8x^2+104 equation:

51-12x=-8x^2+104

We move all terms to the left:

51-12x-(-8x^2+104)=0

We get rid of parentheses

8x^2-12x-104+51=0

We add all the numbers together, and all the variables

8x^2-12x-53=0

a = 8; b = -12; c = -53;
Δ = b2-4ac
Δ = -122-4·8·(-53)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{115}}{2*8}=\frac{12-4\sqrt{115}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{115}}{2*8}=\frac{12+4\sqrt{115}}{16}
$