5x(-2x+14)=10

Solution for 5x(-2x+14)=10 equation:

5x(-2x+14)=10

We move all terms to the left:

5x(-2x+14)-(10)=0

We multiply parentheses

-10x^2+70x-10=0

a = -10; b = 70; c = -10;
Δ = b2-4ac
Δ = 702-4·(-10)·(-10)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-30\sqrt{5}}{2*-10}=\frac{-70-30\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+30\sqrt{5}}{2*-10}=\frac{-70+30\sqrt{5}}{-20}
$