x=7+27x-16X^2

Solution for x=7+27x-16X^2 equation:

x=7+27x-16x^2

We move all terms to the left:

x-(7+27x-16x^2)=0

We get rid of parentheses

16x^2-27x+x-7=0

We add all the numbers together, and all the variables

16x^2-26x-7=0

a = 16; b = -26; c = -7;
Δ = b2-4ac
Δ = -262-4·16·(-7)
Δ = 1124
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:

$\sqrt{\Delta}=\sqrt{1124}=\sqrt{4*281}=\sqrt{4}*\sqrt{281}=2\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{281}}{2*16}=\frac{26-2\sqrt{281}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{281}}{2*16}=\frac{26+2\sqrt{281}}{32}
$