83=3x(x+7)

Solution for 83=3x(x+7) equation:

83=3x(x+7)

We move all terms to the left:

83-(3x(x+7))=0


We calculate terms in parentheses: -(3x(x+7)), so:

3x(x+7)

We multiply parentheses

3x^2+21x

Back to the equation:

-(3x^2+21x)


We get rid of parentheses

-3x^2-21x+83=0

a = -3; b = -21; c = +83;
Δ = b2-4ac
Δ = -212-4·(-3)·83
Δ = 1437
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{1437}}{2*-3}=\frac{21-\sqrt{1437}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1437}}{2*-3}=\frac{21+\sqrt{1437}}{-6}
$