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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4x^2+6x+6x+9)-(5(2x+3))=0


We calculate terms in parentheses: -(5(2x+3)), so:

5(2x+3)

We multiply parentheses

10x+15

Back to the equation:

-(10x+15)


We get rid of parentheses

4x^2+6x+6x-10x+9-15=0

We add all the numbers together, and all the variables

4x^2+2x-6=0

a = 4; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·4·(-6)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*4}=\frac{8}{8}
=1
$