7x*3*5x+x*99x=1

Solution for 7x*3*5x+x*99x=1 equation:

7x*3*5x+x*99x=1

We move all terms to the left:

7x*3*5x+x*99x-(1)=0

Wy multiply elements

105x^2*5+99x^2-1=0

We add all the numbers together, and all the variables

99x^2+105x^2*5-1=0

Wy multiply elements

99x^2+525x^2-1=0

We add all the numbers together, and all the variables

624x^2-1=0

a = 624; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·624·(-1)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{39}}{2*624}=\frac{0-8\sqrt{39}}{1248}
=-\frac{8\sqrt{39}}{1248}
=-\frac{\sqrt{39}}{156}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{39}}{2*624}=\frac{0+8\sqrt{39}}{1248}
=\frac{8\sqrt{39}}{1248}
=\frac{\sqrt{39}}{156}
$