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(x+1)(x-12)=5x
We move all terms to the left:
(x+1)(x-12)-(5x)=0
We add all the numbers together, and all the variables
-5x+(x+1)(x-12)=0
We multiply parentheses ..
(+x^2-12x+x-12)-5x=0
We get rid of parentheses
x^2-12x+x-5x-12=0
We add all the numbers together, and all the variables
x^2-16x-12=0
a = 1; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·1·(-12)
Δ = 304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*1}=\frac{16-4\sqrt{19}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*1}=\frac{16+4\sqrt{19}}{2} $
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