26x+3x^2=665

Solution for 26x+3x^2=665 equation:

26x+3x^2=665

We move all terms to the left:

26x+3x^2-(665)=0

a = 3; b = 26; c = -665;
Δ = b2-4ac
Δ = 262-4·3·(-665)
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-4\sqrt{541}}{2*3}=\frac{-26-4\sqrt{541}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+4\sqrt{541}}{2*3}=\frac{-26+4\sqrt{541}}{6}
$