7x(2x-13)=41

Solution for 7x(2x-13)=41 equation:

7x(2x-13)=41

We move all terms to the left:

7x(2x-13)-(41)=0

We multiply parentheses

14x^2-91x-41=0

a = 14; b = -91; c = -41;
Δ = b2-4ac
Δ = -912-4·14·(-41)
Δ = 10577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-\sqrt{10577}}{2*14}=\frac{91-\sqrt{10577}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{10577}}{2*14}=\frac{91+\sqrt{10577}}{28}
$