(8x-3)(3x+2)-(4x+7)(x+4)=(2x+1)(5x-1)-33

Solution for (8x-3)(3x+2)-(4x+7)(x+4)=(2x+1)(5x-1)-33 equation:

(8x-3)(3x+2)-(4x+7)(x+4)=(2x+1)(5x-1)-33

We move all terms to the left:

(8x-3)(3x+2)-(4x+7)(x+4)-((2x+1)(5x-1)-33)=0

We multiply parentheses ..

(+24x^2+16x-9x-6)-(4x+7)(x+4)-((2x+1)(5x-1)-33)=0


We calculate terms in parentheses: -((2x+1)(5x-1)-33), so:

(2x+1)(5x-1)-33

We multiply parentheses ..

(+10x^2-2x+5x-1)-33

We get rid of parentheses

10x^2-2x+5x-1-33

We add all the numbers together, and all the variables

10x^2+3x-34

Back to the equation:

-(10x^2+3x-34)


We get rid of parentheses

24x^2-10x^2+16x-9x-(4x+7)(x+4)-3x-6+34=0

We multiply parentheses ..

24x^2-10x^2-(+4x^2+16x+7x+28)+16x-9x-3x-6+34=0

We add all the numbers together, and all the variables

14x^2-(+4x^2+16x+7x+28)+4x+28=0

We get rid of parentheses

14x^2-4x^2-16x-7x+4x-28+28=0

We add all the numbers together, and all the variables

10x^2-19x=0

a = 10; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·10·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*10}=\frac{38}{20}
=1+9/10
$