(5x2)=4(2x+3)

Solution for (5x2)=4(2x+3) equation:

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

We move all terms to the left:

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


We calculate terms in parentheses: -(4(2x+3)), so:

4(2x+3)

We multiply parentheses

8x+12

Back to the equation:

-(8x+12)


We get rid of parentheses

5x^2-8x-12=0

a = 5; b = -8; c = -12;
Δ = b2-4ac
Δ = -82-4·5·(-12)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{19}}{2*5}=\frac{8-4\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{19}}{2*5}=\frac{8+4\sqrt{19}}{10}
$