5x2=(2x+1)3

Solution for 5x2=(2x+1)3 equation:

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

We move all terms to the left:

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


We calculate terms in parentheses: -((2x+1)3), so:

(2x+1)3

We multiply parentheses

6x+3

Back to the equation:

-(6x+3)


We get rid of parentheses

5x^2-6x-3=0

a = 5; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·5·(-3)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*5}=\frac{6-4\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*5}=\frac{6+4\sqrt{6}}{10}
$