3x^2+42x-35=0

Solution for 3x^2+42x-35=0 equation:

3x^2+42x-35=0

a = 3; b = 42; c = -35;
Δ = b2-4ac
Δ = 422-4·3·(-35)
Δ = 2184
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:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{546}}{2*3}=\frac{-42-2\sqrt{546}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{546}}{2*3}=\frac{-42+2\sqrt{546}}{6}
$