X=-8x^2+18x+5

Solution for X=-8x^2+18x+5 equation:

X=-8X^2+18X+5

We move all terms to the left:

X-(-8X^2+18X+5)=0

We get rid of parentheses

8X^2-18X+X-5=0

We add all the numbers together, and all the variables

8X^2-17X-5=0

a = 8; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·8·(-5)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{449}}{2*8}=\frac{17-\sqrt{449}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{449}}{2*8}=\frac{17+\sqrt{449}}{16}
$