1.2x(4+5x)=3x(2x+1)-9

Solution for 1.2x(4+5x)=3x(2x+1)-9 equation:

1.2x(4+5x)=3x(2x+1)-9

We move all terms to the left:

1.2x(4+5x)-(3x(2x+1)-9)=0

We add all the numbers together, and all the variables

1.2x(5x+4)-(3x(2x+1)-9)=0

We multiply parentheses

5x^2+4x-(3x(2x+1)-9)=0


We calculate terms in parentheses: -(3x(2x+1)-9), so:

3x(2x+1)-9

We multiply parentheses

6x^2+3x-9

Back to the equation:

-(6x^2+3x-9)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+x+9=0

a = -1; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-1)·9
Δ = 37
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{-(1)-\sqrt{37}}{2*-1}=\frac{-1-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-1}=\frac{-1+\sqrt{37}}{-2}
$