7t^2+4t=5t^2+11t-3

Solution for 7t^2+4t=5t^2+11t-3 equation:

7t^2+4t=5t^2+11t-3

We move all terms to the left:

7t^2+4t-(5t^2+11t-3)=0

We get rid of parentheses

7t^2-5t^2+4t-11t+3=0

We add all the numbers together, and all the variables

2t^2-7t+3=0

a = 2; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·2·3
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{-(-7)-5}{2*2}=\frac{2}{4}
=1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*2}=\frac{12}{4}
=3
$