2a^2=7a+16

Solution for 2a^2=7a+16 equation:

2a^2=7a+16

We move all terms to the left:

2a^2-(7a+16)=0

We get rid of parentheses

2a^2-7a-16=0

a = 2; b = -7; c = -16;
Δ = b2-4ac
Δ = -72-4·2·(-16)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{177}}{2*2}=\frac{7-\sqrt{177}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*2}=\frac{7+\sqrt{177}}{4}
$