16x^2+40x+25=75

Solution for 16x^2+40x+25=75 equation:

16x^2+40x+25=75

We move all terms to the left:

16x^2+40x+25-(75)=0

We add all the numbers together, and all the variables

16x^2+40x-50=0

a = 16; b = 40; c = -50;
Δ = b2-4ac
Δ = 402-4·16·(-50)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{3}}{2*16}=\frac{-40-40\sqrt{3}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{3}}{2*16}=\frac{-40+40\sqrt{3}}{32}
$