0=-4x^2+17x+42

Solution for 0=-4x^2+17x+42 equation:

0=-4x^2+17x+42

We move all terms to the left:

0-(-4x^2+17x+42)=0

We add all the numbers together, and all the variables

-(-4x^2+17x+42)=0

We get rid of parentheses

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