10x(2x+9)=3(15-4x)

Solution for 10x(2x+9)=3(15-4x) equation:

10x(2x+9)=3(15-4x)

We move all terms to the left:

10x(2x+9)-(3(15-4x))=0

We add all the numbers together, and all the variables

10x(2x+9)-(3(-4x+15))=0

We multiply parentheses

20x^2+90x-(3(-4x+15))=0


We calculate terms in parentheses: -(3(-4x+15)), so:

3(-4x+15)

We multiply parentheses

-12x+45

Back to the equation:

-(-12x+45)


We get rid of parentheses

20x^2+90x+12x-45=0

We add all the numbers together, and all the variables

20x^2+102x-45=0

a = 20; b = 102; c = -45;
Δ = b2-4ac
Δ = 1022-4·20·(-45)
Δ = 14004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14004}=\sqrt{36*389}=\sqrt{36}*\sqrt{389}=6\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{389}}{2*20}=\frac{-102-6\sqrt{389}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{389}}{2*20}=\frac{-102+6\sqrt{389}}{40}
$