X(3y+5)+(2y-7)=180

Solution for X(3y+5)+(2y-7)=180 equation:

X(3X+5)+(2X-7)=180

We move all terms to the left:

X(3X+5)+(2X-7)-(180)=0

We multiply parentheses

3X^2+5X+(2X-7)-180=0

We get rid of parentheses

3X^2+5X+2X-7-180=0

We add all the numbers together, and all the variables

3X^2+7X-187=0

a = 3; b = 7; c = -187;
Δ = b2-4ac
Δ = 72-4·3·(-187)
Δ = 2293
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{2293}}{2*3}=\frac{-7-\sqrt{2293}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{2293}}{2*3}=\frac{-7+\sqrt{2293}}{6}
$