(3x^2-1)=(5x+4)

Solution for (3x^2-1)=(5x+4) equation:

(3x^2-1)=(5x+4)

We move all terms to the left:

(3x^2-1)-((5x+4))=0

We get rid of parentheses

3x^2-((5x+4))-1=0


We calculate terms in parentheses: -((5x+4)), so:

(5x+4)

We get rid of parentheses

5x+4

Back to the equation:

-(5x+4)


We get rid of parentheses

3x^2-5x-4-1=0

We add all the numbers together, and all the variables

3x^2-5x-5=0

a = 3; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·3·(-5)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{85}}{2*3}=\frac{5-\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*3}=\frac{5+\sqrt{85}}{6}
$