30x^2-90x=17

Solution for 30x^2-90x=17 equation:

30x^2-90x=17

We move all terms to the left:

30x^2-90x-(17)=0

a = 30; b = -90; c = -17;
Δ = b2-4ac
Δ = -902-4·30·(-17)
Δ = 10140
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:

$\sqrt{\Delta}=\sqrt{10140}=\sqrt{676*15}=\sqrt{676}*\sqrt{15}=26\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-26\sqrt{15}}{2*30}=\frac{90-26\sqrt{15}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+26\sqrt{15}}{2*30}=\frac{90+26\sqrt{15}}{60}
$