75=x(2x-5)

Solution for 75=x(2x-5) equation:

75=x(2x-5)

We move all terms to the left:

75-(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+75=0

a = -2; b = 5; c = +75;
Δ = b2-4ac
Δ = 52-4·(-2)·75
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*-2}=\frac{20}{-4}
=-5
$