4x^2-3x=61

Solution for 4x^2-3x=61 equation:

4x^2-3x=61

We move all terms to the left:

4x^2-3x-(61)=0

a = 4; b = -3; c = -61;
Δ = b2-4ac
Δ = -32-4·4·(-61)
Δ = 985
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{985}}{2*4}=\frac{3-\sqrt{985}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{985}}{2*4}=\frac{3+\sqrt{985}}{8}
$