(8a+6)(9a+10)=304

Solution for (8a+6)(9a+10)=304 equation:

(8a+6)(9a+10)=304

We move all terms to the left:

(8a+6)(9a+10)-(304)=0

We multiply parentheses ..

(+72a^2+80a+54a+60)-304=0

We get rid of parentheses

72a^2+80a+54a+60-304=0

We add all the numbers together, and all the variables

72a^2+134a-244=0

a = 72; b = 134; c = -244;
Δ = b2-4ac
Δ = 1342-4·72·(-244)
Δ = 88228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88228}=\sqrt{4*22057}=\sqrt{4}*\sqrt{22057}=2\sqrt{22057}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-2\sqrt{22057}}{2*72}=\frac{-134-2\sqrt{22057}}{144}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+2\sqrt{22057}}{2*72}=\frac{-134+2\sqrt{22057}}{144}
$