84=x(2x+5)

Solution for 84=x(2x+5) equation:

84=x(2x+5)

We move all terms to the left:

84-(x(2x+5))=0


We calculate terms in parentheses: -(x(2x+5)), so:

x(2x+5)

We multiply parentheses

2x^2+5x

Back to the equation:

-(2x^2+5x)


We get rid of parentheses

-2x^2-5x+84=0

a = -2; b = -5; c = +84;
Δ = b2-4ac
Δ = -52-4·(-2)·84
Δ = 697
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{-(-5)-\sqrt{697}}{2*-2}=\frac{5-\sqrt{697}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{697}}{2*-2}=\frac{5+\sqrt{697}}{-4}
$