10x=13-14x^2

Solution for 10x=13-14x^2 equation:

10x=13-14x^2

We move all terms to the left:

10x-(13-14x^2)=0

We get rid of parentheses

14x^2+10x-13=0

a = 14; b = 10; c = -13;
Δ = b2-4ac
Δ = 102-4·14·(-13)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{23}}{2*14}=\frac{-10-6\sqrt{23}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{23}}{2*14}=\frac{-10+6\sqrt{23}}{28}
$