3x^2+5x+15=(4x+3)(5x+3)

Solution for 3x^2+5x+15=(4x+3)(5x+3) equation:

3x^2+5x+15=(4x+3)(5x+3)

We move all terms to the left:

3x^2+5x+15-((4x+3)(5x+3))=0

We multiply parentheses ..

3x^2-((+20x^2+12x+15x+9))+5x+15=0


We calculate terms in parentheses: -((+20x^2+12x+15x+9)), so:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

20x^2+27x+9

Back to the equation:

-(20x^2+27x+9)


We add all the numbers together, and all the variables

3x^2+5x-(20x^2+27x+9)+15=0

We get rid of parentheses

3x^2-20x^2+5x-27x-9+15=0

We add all the numbers together, and all the variables

-17x^2-22x+6=0

a = -17; b = -22; c = +6;
Δ = b2-4ac
Δ = -222-4·(-17)·6
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{223}}{2*-17}=\frac{22-2\sqrt{223}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{223}}{2*-17}=\frac{22+2\sqrt{223}}{-34}
$