(6x+5)(9x-10)=80

Solution for (6x+5)(9x-10)=80 equation:

(6x+5)(9x-10)=80

We move all terms to the left:

(6x+5)(9x-10)-(80)=0

We multiply parentheses ..

(+54x^2-60x+45x-50)-80=0

We get rid of parentheses

54x^2-60x+45x-50-80=0

We add all the numbers together, and all the variables

54x^2-15x-130=0

a = 54; b = -15; c = -130;
Δ = b2-4ac
Δ = -152-4·54·(-130)
Δ = 28305
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:

$\sqrt{\Delta}=\sqrt{28305}=\sqrt{9*3145}=\sqrt{9}*\sqrt{3145}=3\sqrt{3145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{3145}}{2*54}=\frac{15-3\sqrt{3145}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{3145}}{2*54}=\frac{15+3\sqrt{3145}}{108}
$