3x^2+26x-7=588

Solution for 3x^2+26x-7=588 equation:

3x^2+26x-7=588

We move all terms to the left:

3x^2+26x-7-(588)=0

We add all the numbers together, and all the variables

3x^2+26x-595=0

a = 3; b = 26; c = -595;
Δ = b2-4ac
Δ = 262-4·3·(-595)
Δ = 7816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7816}=\sqrt{4*1954}=\sqrt{4}*\sqrt{1954}=2\sqrt{1954}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1954}}{2*3}=\frac{-26-2\sqrt{1954}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1954}}{2*3}=\frac{-26+2\sqrt{1954}}{6}
$