10x^2+8=-42x

Solution for 10x^2+8=-42x equation:

10x^2+8=-42x

We move all terms to the left:

10x^2+8-(-42x)=0

We get rid of parentheses

10x^2+42x+8=0

a = 10; b = 42; c = +8;
Δ = b2-4ac
Δ = 422-4·10·8
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-38}{2*10}=\frac{-80}{20}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+38}{2*10}=\frac{-4}{20}
=-1/5
$