-5x(2x-9)=-10x+45

Solution for -5x(2x-9)=-10x+45 equation:

-5x(2x-9)=-10x+45

We move all terms to the left:

-5x(2x-9)-(-10x+45)=0

We multiply parentheses

-10x^2+45x-(-10x+45)=0

We get rid of parentheses

-10x^2+45x+10x-45=0

We add all the numbers together, and all the variables

-10x^2+55x-45=0

a = -10; b = 55; c = -45;
Δ = b2-4ac
Δ = 552-4·(-10)·(-45)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-35}{2*-10}=\frac{-90}{-20}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+35}{2*-10}=\frac{-20}{-20}
=1
$