(7x+4)(3x+9)=(4x+3)(3x+5)

Solution for (7x+4)(3x+9)=(4x+3)(3x+5) equation:

(7x+4)(3x+9)=(4x+3)(3x+5)

We move all terms to the left:

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

We multiply parentheses ..

(+21x^2+63x+12x+36)-((4x+3)(3x+5))=0


We calculate terms in parentheses: -((4x+3)(3x+5)), so:

(4x+3)(3x+5)

We multiply parentheses ..

(+12x^2+20x+9x+15)

We get rid of parentheses

12x^2+20x+9x+15

We add all the numbers together, and all the variables

12x^2+29x+15

Back to the equation:

-(12x^2+29x+15)


We get rid of parentheses

21x^2-12x^2+63x+12x-29x+36-15=0

We add all the numbers together, and all the variables

9x^2+46x+21=0

a = 9; b = 46; c = +21;
Δ = b2-4ac
Δ = 462-4·9·21
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-4\sqrt{85}}{2*9}=\frac{-46-4\sqrt{85}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+4\sqrt{85}}{2*9}=\frac{-46+4\sqrt{85}}{18}
$