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3x(x+5)+8=122
We move all terms to the left:
3x(x+5)+8-(122)=0
We add all the numbers together, and all the variables
3x(x+5)-114=0
We multiply parentheses
3x^2+15x-114=0
a = 3; b = 15; c = -114;
Δ = b2-4ac
Δ = 152-4·3·(-114)
Δ = 1593
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{177}}{2*3}=\frac{-15-3\sqrt{177}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{177}}{2*3}=\frac{-15+3\sqrt{177}}{6} $
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