t^2+t-7=-3+4t

Solution for t^2+t-7=-3+4t equation:

t^2+t-7=-3+4t

We move all terms to the left:

t^2+t-7-(-3+4t)=0

We add all the numbers together, and all the variables

t^2+t-(4t-3)-7=0

We get rid of parentheses

t^2+t-4t+3-7=0

We add all the numbers together, and all the variables

t^2-3t-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$