10x2+6=100

Solution for 10x2+6=100 equation:

10x^2+6=100

We move all terms to the left:

10x^2+6-(100)=0

We add all the numbers together, and all the variables

10x^2-94=0

a = 10; b = 0; c = -94;
Δ = b2-4ac
Δ = 02-4·10·(-94)
Δ = 3760
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:

$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{235}}{2*10}=\frac{0-4\sqrt{235}}{20}
=-\frac{4\sqrt{235}}{20}
=-\frac{\sqrt{235}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{235}}{2*10}=\frac{0+4\sqrt{235}}{20}
=\frac{4\sqrt{235}}{20}
=\frac{\sqrt{235}}{5}
$