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 = 6804
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:

$\sqrt{\Delta}=\sqrt{6804}=\sqrt{324*21}=\sqrt{324}*\sqrt{21}=18\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-18\sqrt{21}}{2*20}=\frac{102-18\sqrt{21}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+18\sqrt{21}}{2*20}=\frac{102+18\sqrt{21}}{40}
$