2x(4x-5)=70

Solution for 2x(4x-5)=70 equation:

2x(4x-5)=70

We move all terms to the left:

2x(4x-5)-(70)=0

We multiply parentheses

8x^2-10x-70=0

a = 8; b = -10; c = -70;
Δ = b2-4ac
Δ = -102-4·8·(-70)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{65}}{2*8}=\frac{10-6\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{65}}{2*8}=\frac{10+6\sqrt{65}}{16}
$