3x(x+10)+21=60

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Solution for 3x(x+10)+21=60 equation:



3x(x+10)+21=60
We move all terms to the left:
3x(x+10)+21-(60)=0
We add all the numbers together, and all the variables
3x(x+10)-39=0
We multiply parentheses
3x^2+30x-39=0
a = 3; b = 30; c = -39;
Δ = b2-4ac
Δ = 302-4·3·(-39)
Δ = 1368
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:
$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{38}}{2*3}=\frac{-30-6\sqrt{38}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{38}}{2*3}=\frac{-30+6\sqrt{38}}{6} $

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