(7x-10)(6x-5)=180

Solution for (7x-10)(6x-5)=180 equation:

(7x-10)(6x-5)=180

We move all terms to the left:

(7x-10)(6x-5)-(180)=0

We multiply parentheses ..

(+42x^2-35x-60x+50)-180=0

We get rid of parentheses

42x^2-35x-60x+50-180=0

We add all the numbers together, and all the variables

42x^2-95x-130=0

a = 42; b = -95; c = -130;
Δ = b2-4ac
Δ = -952-4·42·(-130)
Δ = 30865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-\sqrt{30865}}{2*42}=\frac{95-\sqrt{30865}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+\sqrt{30865}}{2*42}=\frac{95+\sqrt{30865}}{84}
$