4t^2-6t-7=0

Solution for 4t^2-6t-7=0 equation:

4t^2-6t-7=0

a = 4; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·4·(-7)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{37}}{2*4}=\frac{6-2\sqrt{37}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{37}}{2*4}=\frac{6+2\sqrt{37}}{8}
$