7x^2+4x=75

Solution for 7x^2+4x=75 equation:

7x^2+4x=75

We move all terms to the left:

7x^2+4x-(75)=0

a = 7; b = 4; c = -75;
Δ = b2-4ac
Δ = 42-4·7·(-75)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-46}{2*7}=\frac{-50}{14}
=-3+4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+46}{2*7}=\frac{42}{14}
=3
$