4x^2+14x=42-3x

Solution for 4x^2+14x=42-3x equation:

4x^2+14x=42-3x

We move all terms to the left:

4x^2+14x-(42-3x)=0

We add all the numbers together, and all the variables

4x^2+14x-(-3x+42)=0

We get rid of parentheses

4x^2+14x+3x-42=0

We add all the numbers together, and all the variables

4x^2+17x-42=0

a = 4; b = 17; c = -42;
Δ = b2-4ac
Δ = 172-4·4·(-42)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*4}=\frac{14}{8}
=1+3/4
$