5x^2=2(4-7x)

Solution for 5x^2=2(4-7x) equation:

5x^2=2(4-7x)

We move all terms to the left:

5x^2-(2(4-7x))=0

We add all the numbers together, and all the variables

5x^2-(2(-7x+4))=0


We calculate terms in parentheses: -(2(-7x+4)), so:

2(-7x+4)

We multiply parentheses

-14x+8

Back to the equation:

-(-14x+8)


We get rid of parentheses

5x^2+14x-8=0

a = 5; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·5·(-8)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{89}}{2*5}=\frac{-14-2\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{89}}{2*5}=\frac{-14+2\sqrt{89}}{10}
$