4x(x+10)+(2x-5)=180

Solution for 4x(x+10)+(2x-5)=180 equation:

4x(x+10)+(2x-5)=180

We move all terms to the left:

4x(x+10)+(2x-5)-(180)=0

We multiply parentheses

4x^2+40x+(2x-5)-180=0

We get rid of parentheses

4x^2+40x+2x-5-180=0

We add all the numbers together, and all the variables

4x^2+42x-185=0

a = 4; b = 42; c = -185;
Δ = b2-4ac
Δ = 422-4·4·(-185)
Δ = 4724
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:

$\sqrt{\Delta}=\sqrt{4724}=\sqrt{4*1181}=\sqrt{4}*\sqrt{1181}=2\sqrt{1181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{1181}}{2*4}=\frac{-42-2\sqrt{1181}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{1181}}{2*4}=\frac{-42+2\sqrt{1181}}{8}
$