4x^2-13x=26

Solution for 4x^2-13x=26 equation:

4x^2-13x=26

We move all terms to the left:

4x^2-13x-(26)=0

a = 4; b = -13; c = -26;
Δ = b2-4ac
Δ = -132-4·4·(-26)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{65}}{2*4}=\frac{13-3\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{65}}{2*4}=\frac{13+3\sqrt{65}}{8}
$