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

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

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

We move all terms to the left:

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

We multiply parentheses

-8x-(-5x(x-2)+2)-12=0


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

-5x(x-2)+2

We multiply parentheses

-5x^2+10x+2

Back to the equation:

-(-5x^2+10x+2)


We get rid of parentheses

5x^2-10x-8x-2-12=0

We add all the numbers together, and all the variables

5x^2-18x-14=0

a = 5; b = -18; c = -14;
Δ = b2-4ac
Δ = -182-4·5·(-14)
Δ = 604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{151}}{2*5}=\frac{18-2\sqrt{151}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{151}}{2*5}=\frac{18+2\sqrt{151}}{10}
$