3(x+3)=5(x^2-1)

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

3(x+3)=5(x^2-1)

We move all terms to the left:

3(x+3)-(5(x^2-1))=0

We multiply parentheses

3x-(5(x^2-1))+9=0


We calculate terms in parentheses: -(5(x^2-1)), so:

5(x^2-1)

We multiply parentheses

5x^2-5

Back to the equation:

-(5x^2-5)


We get rid of parentheses

-5x^2+3x+5+9=0

We add all the numbers together, and all the variables

-5x^2+3x+14=0

a = -5; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-5)·14
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*-5}=\frac{14}{-10}
=-1+2/5
$