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x(x+6)+5(x+5)=42
We move all terms to the left:
x(x+6)+5(x+5)-(42)=0
We multiply parentheses
x^2+6x+5x+25-42=0
We add all the numbers together, and all the variables
x^2+11x-17=0
a = 1; b = 11; c = -17;
Δ = b2-4ac
Δ = 112-4·1·(-17)
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{21}}{2*1}=\frac{-11-3\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{21}}{2*1}=\frac{-11+3\sqrt{21}}{2} $
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