3x^2-40x=75

Solution for 3x^2-40x=75 equation:

3x^2-40x=75

We move all terms to the left:

3x^2-40x-(75)=0

a = 3; b = -40; c = -75;
Δ = b2-4ac
Δ = -402-4·3·(-75)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-50}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+50}{2*3}=\frac{90}{6}
=15
$