x^2+14x+3=2x-3

Solution for x^2+14x+3=2x-3 equation:

x^2+14x+3=2x-3

We move all terms to the left:

x^2+14x+3-(2x-3)=0

We get rid of parentheses

x^2+14x-2x+3+3=0

We add all the numbers together, and all the variables

x^2+12x+6=0

a = 1; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·1·6
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{30}}{2*1}=\frac{-12-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{30}}{2*1}=\frac{-12+2\sqrt{30}}{2}
$