55x*65x=100

Solution for 55x*65x=100 equation:

55x*65x=100

We move all terms to the left:

55x*65x-(100)=0

Wy multiply elements

3575x^2-100=0

a = 3575; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·3575·(-100)
Δ = 1430000
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:

$\sqrt{\Delta}=\sqrt{1430000}=\sqrt{10000*143}=\sqrt{10000}*\sqrt{143}=100\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{143}}{2*3575}=\frac{0-100\sqrt{143}}{7150}
=-\frac{100\sqrt{143}}{7150}
=-\frac{2\sqrt{143}}{143}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{143}}{2*3575}=\frac{0+100\sqrt{143}}{7150}
=\frac{100\sqrt{143}}{7150}
=\frac{2\sqrt{143}}{143}
$