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

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

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

We move all terms to the left:

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

We multiply parentheses

20x^2-40x-(3(3x+2))=0


We calculate terms in parentheses: -(3(3x+2)), so:

3(3x+2)

We multiply parentheses

9x+6

Back to the equation:

-(9x+6)


We get rid of parentheses

20x^2-40x-9x-6=0

We add all the numbers together, and all the variables

20x^2-49x-6=0

a = 20; b = -49; c = -6;
Δ = b2-4ac
Δ = -492-4·20·(-6)
Δ = 2881
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{-(-49)-\sqrt{2881}}{2*20}=\frac{49-\sqrt{2881}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2881}}{2*20}=\frac{49+\sqrt{2881}}{40}
$