23=2t^2+7t+8

Solution for 23=2t^2+7t+8 equation:

23=2t^2+7t+8

We move all terms to the left:

23-(2t^2+7t+8)=0

We get rid of parentheses

-2t^2-7t-8+23=0

We add all the numbers together, and all the variables

-2t^2-7t+15=0

a = -2; b = -7; c = +15;
Δ = b2-4ac
Δ = -72-4·(-2)·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-2}=\frac{20}{-4}
=-5
$