4x^2-3=5(2x-1)

Solution for 4x^2-3=5(2x-1) equation:

4x^2-3=5(2x-1)

We move all terms to the left:

4x^2-3-(5(2x-1))=0


We calculate terms in parentheses: -(5(2x-1)), so:

5(2x-1)

We multiply parentheses

10x-5

Back to the equation:

-(10x-5)


We get rid of parentheses

4x^2-10x+5-3=0

We add all the numbers together, and all the variables

4x^2-10x+2=0

a = 4; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·4·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{17}}{2*4}=\frac{10-2\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{17}}{2*4}=\frac{10+2\sqrt{17}}{8}
$