(4x-1)(5x+3)=-2x(10x-9)

Solution for (4x-1)(5x+3)=-2x(10x-9) equation:

(4x-1)(5x+3)=-2x(10x-9)

We move all terms to the left:

(4x-1)(5x+3)-(-2x(10x-9))=0

We multiply parentheses ..

(+20x^2+12x-5x-3)-(-2x(10x-9))=0


We calculate terms in parentheses: -(-2x(10x-9)), so:

-2x(10x-9)

We multiply parentheses

-20x^2+18x

Back to the equation:

-(-20x^2+18x)


We get rid of parentheses

20x^2+20x^2+12x-5x-18x-3=0

We add all the numbers together, and all the variables

40x^2-11x-3=0

a = 40; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·40·(-3)
Δ = 601
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{-(-11)-\sqrt{601}}{2*40}=\frac{11-\sqrt{601}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{601}}{2*40}=\frac{11+\sqrt{601}}{80}
$