3x^2-14x=75

Solution for 3x^2-14x=75 equation:

3x^2-14x=75

We move all terms to the left:

3x^2-14x-(75)=0

a = 3; b = -14; c = -75;
Δ = b2-4ac
Δ = -142-4·3·(-75)
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{274}}{2*3}=\frac{14-2\sqrt{274}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{274}}{2*3}=\frac{14+2\sqrt{274}}{6}
$