4a-6=-5a2

Solution for 4a-6=-5a2 equation:

4a-6=-5a^2

We move all terms to the left:

4a-6-(-5a^2)=0

We get rid of parentheses

5a^2+4a-6=0

a = 5; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·5·(-6)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{34}}{2*5}=\frac{-4-2\sqrt{34}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{34}}{2*5}=\frac{-4+2\sqrt{34}}{10}
$