X*x+1/8=1512

Solution for X*x+1/8=1512 equation:

X*X+1/8=1512

We move all terms to the left:

X*X+1/8-(1512)=0

determiningTheFunctionDomain
X*X-1512+1/8=0

Wy multiply elements

X^2-1512+1/8=0

We multiply all the terms by the denominator


X^2*8+1-1512*8=0

We add all the numbers together, and all the variables

X^2*8-12095=0

Wy multiply elements

8X^2-12095=0

a = 8; b = 0; c = -12095;
Δ = b2-4ac
Δ = 02-4·8·(-12095)
Δ = 387040
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:

$\sqrt{\Delta}=\sqrt{387040}=\sqrt{16*24190}=\sqrt{16}*\sqrt{24190}=4\sqrt{24190}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{24190}}{2*8}=\frac{0-4\sqrt{24190}}{16}
=-\frac{4\sqrt{24190}}{16}
=-\frac{\sqrt{24190}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{24190}}{2*8}=\frac{0+4\sqrt{24190}}{16}
=\frac{4\sqrt{24190}}{16}
=\frac{\sqrt{24190}}{4}
$