1.4x(x-5)+(x+35)=360

Solution for 1.4x(x-5)+(x+35)=360 equation:

1.4x(x-5)+(x+35)=360

We move all terms to the left:

1.4x(x-5)+(x+35)-(360)=0

We multiply parentheses

x^2-5x+(x+35)-360=0

We get rid of parentheses

x^2-5x+x+35-360=0

We add all the numbers together, and all the variables

x^2-4x-325=0

a = 1; b = -4; c = -325;
Δ = b2-4ac
Δ = -42-4·1·(-325)
Δ = 1316
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:

$\sqrt{\Delta}=\sqrt{1316}=\sqrt{4*329}=\sqrt{4}*\sqrt{329}=2\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{329}}{2*1}=\frac{4-2\sqrt{329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{329}}{2*1}=\frac{4+2\sqrt{329}}{2}
$