(3a+1)=(5a^2+2a-6)

Solution for (3a+1)=(5a^2+2a-6) equation:

(3a+1)=(5a^2+2a-6)

We move all terms to the left:

(3a+1)-((5a^2+2a-6))=0

We get rid of parentheses

3a-((5a^2+2a-6))+1=0


We calculate terms in parentheses: -((5a^2+2a-6)), so:

(5a^2+2a-6)

We get rid of parentheses

5a^2+2a-6

Back to the equation:

-(5a^2+2a-6)


We get rid of parentheses

-5a^2+3a-2a+6+1=0

We add all the numbers together, and all the variables

-5a^2+a+7=0

a = -5; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-5)·7
Δ = 141
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{-(1)-\sqrt{141}}{2*-5}=\frac{-1-\sqrt{141}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*-5}=\frac{-1+\sqrt{141}}{-10}
$