65x*68x=216x+3

Solution for 65x*68x=216x+3 equation:

65x*68x=216x+3

We move all terms to the left:

65x*68x-(216x+3)=0

Wy multiply elements

4420x^2-(216x+3)=0

We get rid of parentheses

4420x^2-216x-3=0

a = 4420; b = -216; c = -3;
Δ = b2-4ac
Δ = -2162-4·4420·(-3)
Δ = 99696
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:

$\sqrt{\Delta}=\sqrt{99696}=\sqrt{16*6231}=\sqrt{16}*\sqrt{6231}=4\sqrt{6231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{6231}}{2*4420}=\frac{216-4\sqrt{6231}}{8840}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{6231}}{2*4420}=\frac{216+4\sqrt{6231}}{8840}
$