8(10^2x-7)=3

Solution for 8(10^2x-7)=3 equation:

8(10^2x-7)=3

We move all terms to the left:

8(10^2x-7)-(3)=0

We multiply parentheses

80x^2-56-3=0

We add all the numbers together, and all the variables

80x^2-59=0

a = 80; b = 0; c = -59;
Δ = b2-4ac
Δ = 02-4·80·(-59)
Δ = 18880
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:

$\sqrt{\Delta}=\sqrt{18880}=\sqrt{64*295}=\sqrt{64}*\sqrt{295}=8\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{295}}{2*80}=\frac{0-8\sqrt{295}}{160}
=-\frac{8\sqrt{295}}{160}
=-\frac{\sqrt{295}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{295}}{2*80}=\frac{0+8\sqrt{295}}{160}
=\frac{8\sqrt{295}}{160}
=\frac{\sqrt{295}}{20}
$