4=5t^2+6t

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

4=5t^2+6t

We move all terms to the left:

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

We get rid of parentheses

-5t^2-6t+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:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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