(x-7)(2x)=15

Solution for (x-7)(2x)=15 equation:

(x-7)(2x)=15

We move all terms to the left:

(x-7)(2x)-(15)=0

We multiply parentheses

2x^2-14x-15=0

a = 2; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·2·(-15)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*2}=\frac{14-2\sqrt{79}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*2}=\frac{14+2\sqrt{79}}{4}
$