(9x+23)(10x+6)=80

Solution for (9x+23)(10x+6)=80 equation:

(9x+23)(10x+6)=80

We move all terms to the left:

(9x+23)(10x+6)-(80)=0

We multiply parentheses ..

(+90x^2+54x+230x+138)-80=0

We get rid of parentheses

90x^2+54x+230x+138-80=0

We add all the numbers together, and all the variables

90x^2+284x+58=0

a = 90; b = 284; c = +58;
Δ = b2-4ac
Δ = 2842-4·90·58
Δ = 59776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{59776}=\sqrt{64*934}=\sqrt{64}*\sqrt{934}=8\sqrt{934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(284)-8\sqrt{934}}{2*90}=\frac{-284-8\sqrt{934}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(284)+8\sqrt{934}}{2*90}=\frac{-284+8\sqrt{934}}{180}
$