3x2=20x-7

Solution for 3x2=20x-7 equation:

3x^2=20x-7

We move all terms to the left:

3x^2-(20x-7)=0

We get rid of parentheses

3x^2-20x+7=0

a = 3; b = -20; c = +7;
Δ = b2-4ac
Δ = -202-4·3·7
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{79}}{2*3}=\frac{20-2\sqrt{79}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{79}}{2*3}=\frac{20+2\sqrt{79}}{6}
$