3(x-2)=-4x(2x+5)=24

Solution for 3(x-2)=-4x(2x+5)=24 equation:

3(x-2)=-4x(2x+5)=24

We move all terms to the left:

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

We multiply parentheses

3x-(-4x(2x+5))-6=0


We calculate terms in parentheses: -(-4x(2x+5)), so:

-4x(2x+5)

We multiply parentheses

-8x^2-20x

Back to the equation:

-(-8x^2-20x)


We get rid of parentheses

8x^2+20x+3x-6=0

We add all the numbers together, and all the variables

8x^2+23x-6=0

a = 8; b = 23; c = -6;
Δ = b2-4ac
Δ = 232-4·8·(-6)
Δ = 721
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{-(23)-\sqrt{721}}{2*8}=\frac{-23-\sqrt{721}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{721}}{2*8}=\frac{-23+\sqrt{721}}{16}
$