10x(3x+2)=9x-(5x-4)

Solution for 10x(3x+2)=9x-(5x-4) equation:

10x(3x+2)=9x-(5x-4)

We move all terms to the left:

10x(3x+2)-(9x-(5x-4))=0

We multiply parentheses

30x^2+20x-(9x-(5x-4))=0


We calculate terms in parentheses: -(9x-(5x-4)), so:

9x-(5x-4)

We get rid of parentheses

9x-5x+4

We add all the numbers together, and all the variables

4x+4

Back to the equation:

-(4x+4)


We get rid of parentheses

30x^2+20x-4x-4=0

We add all the numbers together, and all the variables

30x^2+16x-4=0

a = 30; b = 16; c = -4;
Δ = b2-4ac
Δ = 162-4·30·(-4)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{46}}{2*30}=\frac{-16-4\sqrt{46}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{46}}{2*30}=\frac{-16+4\sqrt{46}}{60}
$