(3a+5)(a-5)=23

Solution for (3a+5)(a-5)=23 equation:

(3a+5)(a-5)=23

We move all terms to the left:

(3a+5)(a-5)-(23)=0

We multiply parentheses ..

(+3a^2-15a+5a-25)-23=0

We get rid of parentheses

3a^2-15a+5a-25-23=0

We add all the numbers together, and all the variables

3a^2-10a-48=0

a = 3; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·3·(-48)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*3}=\frac{-16}{6}
=-2+2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*3}=\frac{36}{6}
=6
$