4x(2x-10)=37

Solution for 4x(2x-10)=37 equation:

4x(2x-10)=37

We move all terms to the left:

4x(2x-10)-(37)=0

We multiply parentheses

8x^2-40x-37=0

a = 8; b = -40; c = -37;
Δ = b2-4ac
Δ = -402-4·8·(-37)
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{174}}{2*8}=\frac{40-4\sqrt{174}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{174}}{2*8}=\frac{40+4\sqrt{174}}{16}
$