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

Solution for 5x(2x+3)-9=4(2+6x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4(6x+2)), so:

4(6x+2)

We multiply parentheses

24x+8

Back to the equation:

-(24x+8)


We get rid of parentheses

10x^2+15x-24x-8-9=0

We add all the numbers together, and all the variables

10x^2-9x-17=0

a = 10; b = -9; c = -17;
Δ = b2-4ac
Δ = -92-4·10·(-17)
Δ = 761
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{-(-9)-\sqrt{761}}{2*10}=\frac{9-\sqrt{761}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{761}}{2*10}=\frac{9+\sqrt{761}}{20}
$