4x^2=-2x+42

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

4x^2=-2x+42

We move all terms to the left:

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

We get rid of parentheses

4x^2+2x-42=0

a = 4; b = 2; c = -42;
Δ = b2-4ac
Δ = 22-4·4·(-42)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26}{2*4}=\frac{24}{8}
=3
$