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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

2x(x+1)-3

We multiply parentheses

2x^2+2x-3

Back to the equation:

-(2x^2+2x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-2)·3
Δ = 33
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{-(3)-\sqrt{33}}{2*-2}=\frac{-3-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*-2}=\frac{-3+\sqrt{33}}{-4}
$