2xx3(5x-7)=47

Solution for 2xx3(5x-7)=47 equation:

2xx3(5x-7)=47

We move all terms to the left:

2xx3(5x-7)-(47)=0

We multiply parentheses

10x^2-14x-47=0

a = 10; b = -14; c = -47;
Δ = b2-4ac
Δ = -142-4·10·(-47)
Δ = 2076
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:

$\sqrt{\Delta}=\sqrt{2076}=\sqrt{4*519}=\sqrt{4}*\sqrt{519}=2\sqrt{519}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{519}}{2*10}=\frac{14-2\sqrt{519}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{519}}{2*10}=\frac{14+2\sqrt{519}}{20}
$