4x^2+100x=360

Solution for 4x^2+100x=360 equation:

4x^2+100x=360

We move all terms to the left:

4x^2+100x-(360)=0

a = 4; b = 100; c = -360;
Δ = b2-4ac
Δ = 1002-4·4·(-360)
Δ = 15760
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:

$\sqrt{\Delta}=\sqrt{15760}=\sqrt{16*985}=\sqrt{16}*\sqrt{985}=4\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{985}}{2*4}=\frac{-100-4\sqrt{985}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{985}}{2*4}=\frac{-100+4\sqrt{985}}{8}
$