164=5x(2x-89)

Solution for 164=5x(2x-89) equation:

164=5x(2x-89)

We move all terms to the left:

164-(5x(2x-89))=0


We calculate terms in parentheses: -(5x(2x-89)), so:

5x(2x-89)

We multiply parentheses

10x^2-445x

Back to the equation:

-(10x^2-445x)


We get rid of parentheses

-10x^2+445x+164=0

a = -10; b = 445; c = +164;
Δ = b2-4ac
Δ = 4452-4·(-10)·164
Δ = 204585
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{-(445)-\sqrt{204585}}{2*-10}=\frac{-445-\sqrt{204585}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(445)+\sqrt{204585}}{2*-10}=\frac{-445+\sqrt{204585}}{-20}
$