3x^2-42x=-87

Solution for 3x^2-42x=-87 equation:

3x^2-42x=-87

We move all terms to the left:

3x^2-42x-(-87)=0

We add all the numbers together, and all the variables

3x^2-42x+87=0

a = 3; b = -42; c = +87;
Δ = b2-4ac
Δ = -422-4·3·87
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-12\sqrt{5}}{2*3}=\frac{42-12\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+12\sqrt{5}}{2*3}=\frac{42+12\sqrt{5}}{6}
$