8x(x-3)+14=2(4x+5)

Solution for 8x(x-3)+14=2(4x+5) equation:

8x(x-3)+14=2(4x+5)

We move all terms to the left:

8x(x-3)+14-(2(4x+5))=0

We multiply parentheses

8x^2-24x-(2(4x+5))+14=0


We calculate terms in parentheses: -(2(4x+5)), so:

2(4x+5)

We multiply parentheses

8x+10

Back to the equation:

-(8x+10)


We get rid of parentheses

8x^2-24x-8x-10+14=0

We add all the numbers together, and all the variables

8x^2-32x+4=0

a = 8; b = -32; c = +4;
Δ = b2-4ac
Δ = -322-4·8·4
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{14}}{2*8}=\frac{32-8\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{14}}{2*8}=\frac{32+8\sqrt{14}}{16}
$