5x^2+14x=75

Solution for 5x^2+14x=75 equation:

5x^2+14x=75

We move all terms to the left:

5x^2+14x-(75)=0

a = 5; b = 14; c = -75;
Δ = b2-4ac
Δ = 142-4·5·(-75)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{106}}{2*5}=\frac{-14-4\sqrt{106}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{106}}{2*5}=\frac{-14+4\sqrt{106}}{10}
$