x^2-3x=4x+14

Solution for x^2-3x=4x+14 equation:

x^2-3x=4x+14

We move all terms to the left:

x^2-3x-(4x+14)=0

We get rid of parentheses

x^2-3x-4x-14=0

We add all the numbers together, and all the variables

x^2-7x-14=0

a = 1; b = -7; c = -14;
Δ = b2-4ac
Δ = -72-4·1·(-14)
Δ = 105
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{105}}{2*1}=\frac{7-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{105}}{2*1}=\frac{7+\sqrt{105}}{2}
$