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6x+x(x-8)=59
We move all terms to the left:
6x+x(x-8)-(59)=0
We multiply parentheses
x^2+6x-8x-59=0
We add all the numbers together, and all the variables
x^2-2x-59=0
a = 1; b = -2; c = -59;
Δ = b2-4ac
Δ = -22-4·1·(-59)
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{15}}{2*1}=\frac{2-4\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{15}}{2*1}=\frac{2+4\sqrt{15}}{2} $
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