X^2+4x^2-12x+36=225

Solution for X^2+4x^2-12x+36=225 equation:

X^2+4X^2-12X+36=225

We move all terms to the left:

X^2+4X^2-12X+36-(225)=0

We add all the numbers together, and all the variables

5X^2-12X-189=0

a = 5; b = -12; c = -189;
Δ = b2-4ac
Δ = -122-4·5·(-189)
Δ = 3924
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:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{109}}{2*5}=\frac{12-6\sqrt{109}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{109}}{2*5}=\frac{12+6\sqrt{109}}{10}
$