6+8x=5x2

Solution for 6+8x=5x2 equation:

6+8x=5x^2

We move all terms to the left:

6+8x-(5x^2)=0

determiningTheFunctionDomain
-5x^2+8x+6=0

a = -5; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·(-5)·6
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*-5}=\frac{-8-2\sqrt{46}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*-5}=\frac{-8+2\sqrt{46}}{-10}
$