(2x)(x-5)=134

Solution for (2x)(x-5)=134 equation:

(2x)(x-5)=134

We move all terms to the left:

(2x)(x-5)-(134)=0

We multiply parentheses

2x^2-10x-134=0

a = 2; b = -10; c = -134;
Δ = b2-4ac
Δ = -102-4·2·(-134)
Δ = 1172
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:

$\sqrt{\Delta}=\sqrt{1172}=\sqrt{4*293}=\sqrt{4}*\sqrt{293}=2\sqrt{293}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{293}}{2*2}=\frac{10-2\sqrt{293}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{293}}{2*2}=\frac{10+2\sqrt{293}}{4}
$