15x^2-51x=-42

Solution for 15x^2-51x=-42 equation:

15x^2-51x=-42

We move all terms to the left:

15x^2-51x-(-42)=0

We add all the numbers together, and all the variables

15x^2-51x+42=0

a = 15; b = -51; c = +42;
Δ = b2-4ac
Δ = -512-4·15·42
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-9}{2*15}=\frac{42}{30}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+9}{2*15}=\frac{60}{30}
=2
$