X+150=3x2+23

Solution for X+150=3x2+23 equation:

X+150=3X^2+23

We move all terms to the left:

X+150-(3X^2+23)=0

We get rid of parentheses

-3X^2+X-23+150=0

We add all the numbers together, and all the variables

-3X^2+X+127=0

a = -3; b = 1; c = +127;
Δ = b2-4ac
Δ = 12-4·(-3)·127
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{61}}{2*-3}=\frac{-1-5\sqrt{61}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{61}}{2*-3}=\frac{-1+5\sqrt{61}}{-6}
$