9x^2-42x=15

Solution for 9x^2-42x=15 equation:

9x^2-42x=15

We move all terms to the left:

9x^2-42x-(15)=0

a = 9; b = -42; c = -15;
Δ = b2-4ac
Δ = -422-4·9·(-15)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-48}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+48}{2*9}=\frac{90}{18}
=5
$