4x^2-3x=75

Solution for 4x^2-3x=75 equation:

4x^2-3x=75

We move all terms to the left:

4x^2-3x-(75)=0

a = 4; b = -3; c = -75;
Δ = b2-4ac
Δ = -32-4·4·(-75)
Δ = 1209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1209}}{2*4}=\frac{3-\sqrt{1209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1209}}{2*4}=\frac{3+\sqrt{1209}}{8}
$