(9x-4)(2x-6)+(7x-3)(x+5)-(5+3)(5x-1)=4

Solution for (9x-4)(2x-6)+(7x-3)(x+5)-(5+3)(5x-1)=4 equation:

(9x-4)(2x-6)+(7x-3)(x+5)-(5+3)(5x-1)=4

We move all terms to the left:

(9x-4)(2x-6)+(7x-3)(x+5)-(5+3)(5x-1)-(4)=0

We add all the numbers together, and all the variables

(9x-4)(2x-6)+(7x-3)(x+5)-8(5x-1)-4=0

We multiply parentheses

(9x-4)(2x-6)+(7x-3)(x+5)-40x+8-4=0

We multiply parentheses ..

(+18x^2-54x-8x+24)+(7x-3)(x+5)-40x+8-4=0

We add all the numbers together, and all the variables

(+18x^2-54x-8x+24)-40x+(7x-3)(x+5)+4=0

We get rid of parentheses

18x^2-54x-8x-40x+(7x-3)(x+5)+24+4=0

We multiply parentheses ..

18x^2+(+7x^2+35x-3x-15)-54x-8x-40x+24+4=0

We add all the numbers together, and all the variables

18x^2+(+7x^2+35x-3x-15)-102x+28=0

We get rid of parentheses

18x^2+7x^2+35x-3x-102x-15+28=0

We add all the numbers together, and all the variables

25x^2-70x+13=0

a = 25; b = -70; c = +13;
Δ = b2-4ac
Δ = -702-4·25·13
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-60}{2*25}=\frac{10}{50}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+60}{2*25}=\frac{130}{50}
=2+3/5
$