2x(5-3x)=(7x-4)-(8x-9)

Solution for 2x(5-3x)=(7x-4)-(8x-9) equation:

2x(5-3x)=(7x-4)-(8x-9)

We move all terms to the left:

2x(5-3x)-((7x-4)-(8x-9))=0

We add all the numbers together, and all the variables

2x(-3x+5)-((7x-4)-(8x-9))=0

We multiply parentheses

-6x^2+10x-((7x-4)-(8x-9))=0


We calculate terms in parentheses: -((7x-4)-(8x-9)), so:

(7x-4)-(8x-9)

We get rid of parentheses

7x-8x-4+9

We add all the numbers together, and all the variables

-1x+5

Back to the equation:

-(-1x+5)


We get rid of parentheses

-6x^2+10x+1x-5=0

We add all the numbers together, and all the variables

-6x^2+11x-5=0

a = -6; b = 11; c = -5;
Δ = b2-4ac
Δ = 112-4·(-6)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*-6}=\frac{-10}{-12}
=5/6
$