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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2+12x-((2x-5))=0


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

(2x-5)

We get rid of parentheses

2x-5

Back to the equation:

-(2x-5)


We get rid of parentheses

4x^2+12x-2x+5=0

We add all the numbers together, and all the variables

4x^2+10x+5=0

a = 4; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·4·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*4}=\frac{-10-2\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*4}=\frac{-10+2\sqrt{5}}{8}
$