6x+4=5x^2

Solution for 6x+4=5x^2 equation:

6x+4=5x^2

We move all terms to the left:

6x+4-(5x^2)=0

determiningTheFunctionDomain
-5x^2+6x+4=0

a = -5; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-5)·4
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*-5}=\frac{-6-2\sqrt{29}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*-5}=\frac{-6+2\sqrt{29}}{-10}
$