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

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

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

We move all terms to the left:

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

We multiply parentheses

-5a^2+10a-(4(-2a-3))+2=0


We calculate terms in parentheses: -(4(-2a-3)), so:

4(-2a-3)

We multiply parentheses

-8a-12

Back to the equation:

-(-8a-12)


We get rid of parentheses

-5a^2+10a+8a+12+2=0

We add all the numbers together, and all the variables

-5a^2+18a+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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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