(x+10)(4x-35)=180

Solution for (x+10)(4x-35)=180 equation:

(x+10)(4x-35)=180

We move all terms to the left:

(x+10)(4x-35)-(180)=0

We multiply parentheses ..

(+4x^2-35x+40x-350)-180=0

We get rid of parentheses

4x^2-35x+40x-350-180=0

We add all the numbers together, and all the variables

4x^2+5x-530=0

a = 4; b = 5; c = -530;
Δ = b2-4ac
Δ = 52-4·4·(-530)
Δ = 8505
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:

$\sqrt{\Delta}=\sqrt{8505}=\sqrt{81*105}=\sqrt{81}*\sqrt{105}=9\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9\sqrt{105}}{2*4}=\frac{-5-9\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9\sqrt{105}}{2*4}=\frac{-5+9\sqrt{105}}{8}
$