X=3y(4y+5)-2

Solution for X=3y(4y+5)-2 equation:

X=3X(4X+5)-2

We move all terms to the left:

X-(3X(4X+5)-2)=0


We calculate terms in parentheses: -(3X(4X+5)-2), so:

3X(4X+5)-2

We multiply parentheses

12X^2+15X-2

Back to the equation:

-(12X^2+15X-2)


We get rid of parentheses

-12X^2+X-15X+2=0

We add all the numbers together, and all the variables

-12X^2-14X+2=0

a = -12; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·(-12)·2
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*-12}=\frac{14-2\sqrt{73}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*-12}=\frac{14+2\sqrt{73}}{-24}
$