10+7x2=34

Solution for 10+7x2=34 equation:

10+7x^2=34

We move all terms to the left:

10+7x^2-(34)=0

We add all the numbers together, and all the variables

7x^2-24=0

a = 7; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·7·(-24)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*7}=\frac{0-4\sqrt{42}}{14}
=-\frac{4\sqrt{42}}{14}
=-\frac{2\sqrt{42}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*7}=\frac{0+4\sqrt{42}}{14}
=\frac{4\sqrt{42}}{14}
=\frac{2\sqrt{42}}{7}
$