x2-18x+14=-9-4

Solution for x2-18x+14=-9-4 equation:

x2-18x+14=-9-4

We move all terms to the left:

x2-18x+14-(-9-4)=0

We add all the numbers together, and all the variables

x2-18x+14-(-13)=0

We add all the numbers together, and all the variables

x^2-18x+27=0

a = 1; b = -18; c = +27;
Δ = b2-4ac
Δ = -182-4·1·27
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{6}}{2*1}=\frac{18-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{6}}{2*1}=\frac{18+6\sqrt{6}}{2}
$