4(2a+3)=-3a(a-1)+31

Solution for 4(2a+3)=-3a(a-1)+31 equation:

4(2a+3)=-3a(a-1)+31

We move all terms to the left:

4(2a+3)-(-3a(a-1)+31)=0

We multiply parentheses

8a-(-3a(a-1)+31)+12=0


We calculate terms in parentheses: -(-3a(a-1)+31), so:

-3a(a-1)+31

We multiply parentheses

-3a^2+3a+31

Back to the equation:

-(-3a^2+3a+31)


We get rid of parentheses

3a^2-3a+8a-31+12=0

We add all the numbers together, and all the variables

3a^2+5a-19=0

a = 3; b = 5; c = -19;
Δ = b2-4ac
Δ = 52-4·3·(-19)
Δ = 253
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{253}}{2*3}=\frac{-5-\sqrt{253}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{253}}{2*3}=\frac{-5+\sqrt{253}}{6}
$