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3x(x+5)-6=18
We move all terms to the left:
3x(x+5)-6-(18)=0
We add all the numbers together, and all the variables
3x(x+5)-24=0
We multiply parentheses
3x^2+15x-24=0
a = 3; b = 15; c = -24;
Δ = b2-4ac
Δ = 152-4·3·(-24)
Δ = 513
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{57}}{2*3}=\frac{-15-3\sqrt{57}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{57}}{2*3}=\frac{-15+3\sqrt{57}}{6} $
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