144+10x=32x^2

Solution for 144+10x=32x^2 equation:

144+10x=32x^2

We move all terms to the left:

144+10x-(32x^2)=0

determiningTheFunctionDomain
-32x^2+10x+144=0

a = -32; b = 10; c = +144;
Δ = b2-4ac
Δ = 102-4·(-32)·144
Δ = 18532
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:

$\sqrt{\Delta}=\sqrt{18532}=\sqrt{4*4633}=\sqrt{4}*\sqrt{4633}=2\sqrt{4633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{4633}}{2*-32}=\frac{-10-2\sqrt{4633}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{4633}}{2*-32}=\frac{-10+2\sqrt{4633}}{-64}
$