2x^2+144=-34x

Solution for 2x^2+144=-34x equation:

2x^2+144=-34x

We move all terms to the left:

2x^2+144-(-34x)=0

We get rid of parentheses

2x^2+34x+144=0

a = 2; b = 34; c = +144;
Δ = b2-4ac
Δ = 342-4·2·144
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2}{2*2}=\frac{-32}{4}
=-8
$