(9x+10)(7x+2)=180

Solution for (9x+10)(7x+2)=180 equation:

(9x+10)(7x+2)=180

We move all terms to the left:

(9x+10)(7x+2)-(180)=0

We multiply parentheses ..

(+63x^2+18x+70x+20)-180=0

We get rid of parentheses

63x^2+18x+70x+20-180=0

We add all the numbers together, and all the variables

63x^2+88x-160=0

a = 63; b = 88; c = -160;
Δ = b2-4ac
Δ = 882-4·63·(-160)
Δ = 48064
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:

$\sqrt{\Delta}=\sqrt{48064}=\sqrt{64*751}=\sqrt{64}*\sqrt{751}=8\sqrt{751}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8\sqrt{751}}{2*63}=\frac{-88-8\sqrt{751}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8\sqrt{751}}{2*63}=\frac{-88+8\sqrt{751}}{126}
$