5(x^2)=3x+21

Solution for 5(x^2)=3x+21 equation:

5(x^2)=3x+21

We move all terms to the left:

5(x^2)-(3x+21)=0

We get rid of parentheses

5x^2-3x-21=0

a = 5; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·5·(-21)
Δ = 429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{429}}{2*5}=\frac{3-\sqrt{429}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{429}}{2*5}=\frac{3+\sqrt{429}}{10}
$