3-(8x-5)+(6-7x)+3=7x(5x+9-3)

Solution for 3-(8x-5)+(6-7x)+3=7x(5x+9-3) equation:

3-(8x-5)+(6-7x)+3=7x(5x+9-3)

We move all terms to the left:

3-(8x-5)+(6-7x)+3-(7x(5x+9-3))=0

We add all the numbers together, and all the variables

-(8x-5)+(-7x+6)-(7x(5x+6))+3+3=0

We add all the numbers together, and all the variables

-(8x-5)+(-7x+6)-(7x(5x+6))+6=0

We get rid of parentheses

-8x-7x-(7x(5x+6))+5+6+6=0


We calculate terms in parentheses: -(7x(5x+6)), so:

7x(5x+6)

We multiply parentheses

35x^2+42x

Back to the equation:

-(35x^2+42x)


We add all the numbers together, and all the variables

-15x-(35x^2+42x)+17=0

We get rid of parentheses

-35x^2-15x-42x+17=0

We add all the numbers together, and all the variables

-35x^2-57x+17=0

a = -35; b = -57; c = +17;
Δ = b2-4ac
Δ = -572-4·(-35)·17
Δ = 5629
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{-(-57)-\sqrt{5629}}{2*-35}=\frac{57-\sqrt{5629}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{5629}}{2*-35}=\frac{57+\sqrt{5629}}{-70}
$