4t^2/5=2t+3

Solution for 4t^2/5=2t+3 equation:

4t^2/5=2t+3

We move all terms to the left:

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

We get rid of parentheses

4t^2/5-2t-3=0

We multiply all the terms by the denominator


4t^2-2t*5-3*5=0

We add all the numbers together, and all the variables

4t^2-2t*5-15=0

Wy multiply elements

4t^2-10t-15=0

a = 4; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·4·(-15)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*4}=\frac{10-2\sqrt{85}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*4}=\frac{10+2\sqrt{85}}{8}
$