20.5=(x)(2x+5)

Solution for 20.5=(x)(2x+5) equation:

20.5=(x)(2x+5)

We move all terms to the left:

20.5-((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+20.5=0

a = -2; b = -5; c = +20.5;
Δ = b2-4ac
Δ = -52-4·(-2)·20.5
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{21}}{2*-2}=\frac{5-3\sqrt{21}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{21}}{2*-2}=\frac{5+3\sqrt{21}}{-4}
$