(x-3)(x-8)=201+5x

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Solution for (x-3)(x-8)=201+5x equation:



(x-3)(x-8)=201+5x
We move all terms to the left:
(x-3)(x-8)-(201+5x)=0
We add all the numbers together, and all the variables
(x-3)(x-8)-(5x+201)=0
We get rid of parentheses
(x-3)(x-8)-5x-201=0
We multiply parentheses ..
(+x^2-8x-3x+24)-5x-201=0
We get rid of parentheses
x^2-8x-3x-5x+24-201=0
We add all the numbers together, and all the variables
x^2-16x-177=0
a = 1; b = -16; c = -177;
Δ = b2-4ac
Δ = -162-4·1·(-177)
Δ = 964
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:
$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{241}}{2*1}=\frac{16-2\sqrt{241}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{241}}{2*1}=\frac{16+2\sqrt{241}}{2} $

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