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

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

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

We move all terms to the left:

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


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

(9x+3)

We get rid of parentheses

9x+3

Back to the equation:

-(9x+3)


We get rid of parentheses

45x^2-9x-3=0

a = 45; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·45·(-3)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{69}}{2*45}=\frac{9-3\sqrt{69}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{69}}{2*45}=\frac{9+3\sqrt{69}}{90}
$