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

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

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

We move all terms to the left:

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

We multiply parentheses

4x-(5(x+3)x)+6=0


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

5(x+3)x

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

-5x^2+4x-15x+6=0

We add all the numbers together, and all the variables

-5x^2-11x+6=0

a = -5; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·(-5)·6
Δ = 241
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{-(-11)-\sqrt{241}}{2*-5}=\frac{11-\sqrt{241}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*-5}=\frac{11+\sqrt{241}}{-10}
$