4x^2-5x-14=7+3x

Solution for 4x^2-5x-14=7+3x equation:

4x^2-5x-14=7+3x

We move all terms to the left:

4x^2-5x-14-(7+3x)=0

We add all the numbers together, and all the variables

4x^2-5x-(3x+7)-14=0

We get rid of parentheses

4x^2-5x-3x-7-14=0

We add all the numbers together, and all the variables

4x^2-8x-21=0

a = 4; b = -8; c = -21;
Δ = b2-4ac
Δ = -82-4·4·(-21)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*4}=\frac{28}{8}
=3+1/2
$