X^2+5x-12=3x+1

Solution for X^2+5x-12=3x+1 equation:

X^2+5X-12=3X+1

We move all terms to the left:

X^2+5X-12-(3X+1)=0

We get rid of parentheses

X^2+5X-3X-1-12=0

We add all the numbers together, and all the variables

X^2+2X-13=0

a = 1; b = 2; c = -13;
Δ = b2-4ac
Δ = 22-4·1·(-13)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{14}}{2*1}=\frac{-2-2\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{14}}{2*1}=\frac{-2+2\sqrt{14}}{2}
$