10x^2-54x-81=25

Solution for 10x^2-54x-81=25 equation:

10x^2-54x-81=25

We move all terms to the left:

10x^2-54x-81-(25)=0

We add all the numbers together, and all the variables

10x^2-54x-106=0

a = 10; b = -54; c = -106;
Δ = b2-4ac
Δ = -542-4·10·(-106)
Δ = 7156
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:

$\sqrt{\Delta}=\sqrt{7156}=\sqrt{4*1789}=\sqrt{4}*\sqrt{1789}=2\sqrt{1789}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1789}}{2*10}=\frac{54-2\sqrt{1789}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1789}}{2*10}=\frac{54+2\sqrt{1789}}{20}
$