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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2-10x-4x-20-10=0

We add all the numbers together, and all the variables

2x^2-14x-30=0

a = 2; b = -14; c = -30;
Δ = b2-4ac
Δ = -142-4·2·(-30)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{109}}{2*2}=\frac{14-2\sqrt{109}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{109}}{2*2}=\frac{14+2\sqrt{109}}{4}
$