7t+16t^2=23

Solution for 7t+16t^2=23 equation:

7t+16t^2=23

We move all terms to the left:

7t+16t^2-(23)=0

a = 16; b = 7; c = -23;
Δ = b2-4ac
Δ = 72-4·16·(-23)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-39}{2*16}=\frac{-46}{32}
=-1+7/16
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+39}{2*16}=\frac{32}{32}
=1
$