29x^2-122x+90=25765

Solution for 29x^2-122x+90=25765 equation:

29x^2-122x+90=25765

We move all terms to the left:

29x^2-122x+90-(25765)=0

We add all the numbers together, and all the variables

29x^2-122x-25675=0

a = 29; b = -122; c = -25675;
Δ = b2-4ac
Δ = -1222-4·29·(-25675)
Δ = 2993184
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:

$\sqrt{\Delta}=\sqrt{2993184}=\sqrt{144*20786}=\sqrt{144}*\sqrt{20786}=12\sqrt{20786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-12\sqrt{20786}}{2*29}=\frac{122-12\sqrt{20786}}{58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+12\sqrt{20786}}{2*29}=\frac{122+12\sqrt{20786}}{58}
$