84=x(2x+13)

Solution for 84=x(2x+13) equation:

84=x(2x+13)

We move all terms to the left:

84-(x(2x+13))=0


We calculate terms in parentheses: -(x(2x+13)), so:

x(2x+13)

We multiply parentheses

2x^2+13x

Back to the equation:

-(2x^2+13x)


We get rid of parentheses

-2x^2-13x+84=0

a = -2; b = -13; c = +84;
Δ = b2-4ac
Δ = -132-4·(-2)·84
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*-2}=\frac{42}{-4}
=-10+1/2
$