4(5x2)=2(9x+3)

Solution for 4(5x2)=2(9x+3) equation:

4(5x^2)=2(9x+3)

We move all terms to the left:

4(5x^2)-(2(9x+3))=0


We calculate terms in parentheses: -(2(9x+3)), so:

2(9x+3)

We multiply parentheses

18x+6

Back to the equation:

-(18x+6)


We get rid of parentheses

45x^2-18x-6=0

a = 45; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·45·(-6)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{39}}{2*45}=\frac{18-6\sqrt{39}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{39}}{2*45}=\frac{18+6\sqrt{39}}{90}
$