-2x(x-10)=3(x-30)

Solution for -2x(x-10)=3(x-30) equation:

-2x(x-10)=3(x-30)

We move all terms to the left:

-2x(x-10)-(3(x-30))=0

We multiply parentheses

-2x^2+20x-(3(x-30))=0


We calculate terms in parentheses: -(3(x-30)), so:

3(x-30)

We multiply parentheses

3x-90

Back to the equation:

-(3x-90)


We get rid of parentheses

-2x^2+20x-3x+90=0

We add all the numbers together, and all the variables

-2x^2+17x+90=0

a = -2; b = 17; c = +90;
Δ = b2-4ac
Δ = 172-4·(-2)·90
Δ = 1009
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{-(17)-\sqrt{1009}}{2*-2}=\frac{-17-\sqrt{1009}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{1009}}{2*-2}=\frac{-17+\sqrt{1009}}{-4}
$